Hello and welcome to lecture 6 of this lecture series on Introduction to Aerospace Propulsion. In the previous lectures, we have looked at different aspects of very fundamental thermodynamics like defining very basic terms which are to be used throughout this course of thermodynamics. So, in this particular lecture, we are going to take it forward and look at some more aspects of basic thermodynamic interactions. So, let us take a look at what we are going to get introduced to in this particular lecture. Now, in this lecture, what we are going to look at are the following. We shall at the beginning understand what is meant by specific heat. We shall define specific heat and also define specific heat for two different cases or specific heat in two different forms known as specific heat at constant pressure and specific heat at constant volume. Subsequently, we shall look at different forms or modes of energy interactions. One of them is heat transfer. We shall understand the thermodynamic meaning of heat transfer and also look at the types of heat transfer. And then, we shall look at the other type of energy interaction that is known as work. We shall understand the basic meaning or thermodynamic meaning of work and also look at different types of work interactions. Now, as we are already aware that it takes different amounts of heat or energy to raise the temperature of a given substance or identical masses of different substances. For example, if you would like to raise the heat of water by a particular temperature and if you would like to the same amount or same mass of let us say iron to be heated to the same temperature, then we know that it takes different amounts of heat. So, based on this property, we shall define what is known as specific heat. And so, specific heat is a property that helps us in understanding how much is the amount of temperature or energy required to raise the temperature of identical masses. So, therefore, it is desirable that we have a property that will enable us to compare the energy storage capabilities of different substances. And this property is what we shall define as specific heat. So, specific heat by definition is the energy required to raise the temperature of a unit mass of a substance by one degree. And in general, this energy depends upon how this process is executed. And based on this, we can define two kinds of specific heat. One is known as specific heat at constant volume and the other is known as specific heat at constant pressure. Now, if you were to look at specific heat as a property which we shall see very shortly, that specific heat is basically a property of a system. As we have already seen, properties are certain characteristics that define the state of a particular system. Now, let us look at an example of how we can define specific heat for a particular substance for a particular process. Now, what is shown here is a particular mass which is let us say 1 kg's and we have to increase its temperature by delta t which is equal to 1 degree Celsius. And if this is the case, then we will need 5 kilo joules of energy for example, to accomplish this that is to raise the mass of 1 kg by 1 degree Celsius. And therefore, specific heat here would be the amount of energy here required to raise the temperature of a unit mass which is 1 kg here by 1 degree Celsius in a specific way. And therefore, the specific heat for this particular process will be 5 kilo joules per kilogram degree Celsius. And so, this is how one would define specific heat for a particular process. And now, let us now consider a fixed stationary mass of a closed system undergoing let us say a constant volume process. As I had already mentioned that specific heat can be defined in two different ways depending upon how the process is carried out. One of them is known as specific heat at constant volume and the other is known as specific heat at constant pressure. So, let us now define specific heat at constant volume and also find specific heat at constant volume in terms of known properties. Now, for this purpose let us now consider a stationary mass of a particular system of a closed system which is at constant volume. Now, we already know that you perhaps are aware of the conservation of energy principle. Now, if you were to apply conservation of energy principle which we shall see in much detail little later as well. Then, conservation of energy principle for this process is expressed in a differential form as shown here. Now, this differential form of expressing the conservation of energy principle leads us to this equation which is delta E in minus delta E out is equal to d u. As we have seen earlier that for a stationary system the net change in energy for the system because it is stationary will be equal to the change in its internal energy because kinetic energy and potential energy changes are 0 and therefore, as we had seen in the previous lecture delta E will be equal to delta u. So, this is the same equation that we have expressed in a slightly different form. Now, let us look at this equation once again d E in minus d E out is equal to d u. Now, this left hand side of this equation as I was just mentioning represents the net amount of energy transferred to the system because it is delta E in minus delta E in out which is essentially the net amount of energy which is transferred to the system. And therefore, the left hand side is actually equal to C v times d t because C v is specific heat at constant volume and as per the definition of specific heat it is the amount of energy required to raise the temperature of a unit mass of a substance by unit degree rise. And therefore, left hand side of the equation is equal to C v times d t which is equal to d u. And therefore, specific heat at constant volume which is denoted by C subscript v is equal to del u by del t at constant v. So, specific heat at constant volume is defined in terms of two properties of a system which is internal energy and temperature and del u by del t at constant volume gives a specific heat at constant volume that is C v. Now, the other property which I had mentioned as specific heat at constant pressure can also be derived in a very similar fashion. So, for deriving C p we would be considering a constant pressure process it could be either an expansion process or it could be a compression process. So, if you were to do a similar exercise as we did for C v then we get C p d t is equal to d h or C p is equal to del h by del t at constant p. Again as you can see here specific heat at constant pressure is again a function of two properties of a system that is enthalpy and temperature defined at constant pressure. Specific heat at constant volume is a function of two other properties of a system the internal energy u and the temperature t and since both of these depend on properties of system it is obvious that C p and C v have to be properties of a system. They are properties of a system because they depend on different properties of a particular system for example, C p depends upon the enthalpy and temperature and C v depends upon the internal energy and temperature which means that both C p and C v are properties of a system. And both C p and C v definitions though we had used or we had defined these properties for constant pressure and constant volume these are valid for any other processes it can be shown that C p and C v would be valid for any other process. And it is also a fact that specific heat at constant pressure C p is always greater in terms of its magnitude than specific heat at constant volume C v. Basically the reason for this is that if you were to carry out a process at constant pressure we have to allow the system to expand which means that you have to spend additional energy for this particular expansion of a system which is not there in the case of a constant volume process. So, if the volume were to be constant then there is no more expansion or compression of a system. So, the system does not require additional energy for expanding against the atmosphere. And therefore, because in a C p process that is constant pressure process you will need additional energy to keep the pressure a constant to allow for the system to expand. And therefore, C p is always greater than C v and specific heat of a substance will change with temperature which also will be clear in one of the examples which I shall show little later. Now, as I was mentioning C p is always greater than C v let us look at why is that so. Now, on the left hand side you can see a system which is enclosed in a chamber and therefore, its volume is constant. And let us say its mass is 1 kg and we have to raise the temperature by 1 degree Celsius. And for that to happen we have to supply this is just an example we have to supply for example, an energy equivalent to 3.12 kilo joules. And therefore, the C v would be 3.12 kilo joules per kilogram degree Celsius. Now, if the same system one of the boundaries let us say the upper boundary were to be movable that can convert the system into a moving boundary closed system. And if this were to be the case as you transfer energy to the system the system will expand which means that its volume will keep increasing, but the pressure would remain the same we can keep the pressure a constant. Now, in this case in addition to transferring energy to raise the temperature by 1 degree Celsius you need additional energy to account for this expansion process. And therefore, that is reflected in the additional energy which you can see here that in this example we have an energy of 5.19 kilo joules. Therefore, C p would be 5.19 kilo joules per kilogram degree Celsius. And this is why specific heat at constant pressure will always be greater than specific heat at constant volume. Now, the other point I was mentioning was that specific heat of a substance will change with temperature. To illustrate this let us look at another example let us consider air which is enclosed in a closed volume which has a mass of 1 kg. Let us say we have to raise the temperature of air from 300 Kelvin to 301 Kelvin. So, for this process we would probably require an energy of about 0.718 kilo joules. Now, if we were to consider the same system which is initially at a higher temperature of let us say 1000 Kelvin and we have to raise it to 1001 Kelvin we will need additional amount of energy that is amount of energy required to raise this unit mass of 1 k g by 1 Kelvin which was initially at a higher temperature than the previous case will require more energy that means the specific heat in the second case will be greater than the specific heat in the previous case. Therefore, specific heat of a substance will always change with temperature specific heat is a function a strong function of temperature. And in many of the practical engineering calculations this has to be taken into account because for simplistic calculations we normally assume that specific heat does not change with temperature but that is restricted to very simple calculations as we go towards more and more complex calculations which are actually required in engineering applications. We have to take this variation of specific heat with temperature into account and perhaps in later lectures we would take a look at some examples where we shall see how much difference we get by using specific by assuming specific heat to remain the same for different temperatures. And also looking at how specific heat changes with temperature for different cases and we shall compare the difference between the results we get from these two calculations and we shall see that for practical applications it does make a lot of difference. So, what we have defined now are two different properties of a system specific heat at constant pressure and specific heat at constant volume and we shall see little later that these are very important properties of a system which have lot of practical significance and we shall be using both these properties very frequently when we do engineering analysis of different systems. So, what we shall see next is two different energy transfer mechanisms one of them is known as heat and the other is known as work. So, energy can cross the system boundaries of a closed system in two modes one mode is known as heat and the other mode is known as work. So, what is shown here as an illustration is a system a closed system which has a mass equal to constant there can be two modes of energy transfer or energy interaction across these system boundaries. And both of them are as we shall see little later known as path functions we will define path functions little later. So, there are two different energy interactions possible one is known as heat and the other is known as work. And we shall see in the next lecture that for an open system there is one more form of energy interaction that is through mass flow rate. So, for a closed system there are two forms of energy interactions now let us look at the one of the forms of energy interaction known as heat. Now, as we have or as you are probably aware or we refer to heat on a day to day basis for example, we say some on a particular day that if it is a hot humid day we say the heat is very high and so on. So, heat is a term which is very commonly used in our day to day lives, but thermodynamically it might mean slightly different it might be used in slightly different context. So, heat is if you were to define thermodynamically is a form of energy that is transferred between two systems or a system and its surroundings by virtue of a temperature difference. So, the energy interaction that takes place between either two systems or between a system and its surroundings by virtue of its by virtue of a temperature difference is known as heat. And therefore, energy interaction is classified as heat or is qualified as heat only if it takes place by virtue of its temperature difference. And therefore, it is obvious to state that heat is energy in transition and therefore, heat is recognized only as it crosses a system boundary. So, thermodynamically heat is a form of energy which gets transferred between two systems or between a system and its surroundings by virtue of a temperature difference. And therefore, that is the thermodynamic definition of heat. Now, let us look at an example here. Now, we have three different systems well it is the same system at three different temperatures. In the first case we have the system at 25 degree Celsius we may consider the system as let us say a cup of cold coffee or let us say a can of cold drink or something like that which is in the first case let us say the system has the same temperature as the ambient. Let us say the ambient air or the room air is also at 25 degree Celsius. If the system is also at the same temperature as that of the room then there is no heat transfer which takes place between the system and the surroundings. Now, if the system were at a lower temperature of let us say 15 degree Celsius then there is definitely a heat transfer from the surroundings to the system because the surrounding air temperature is higher than the system temperature and therefore, there is a heat transfer from the surroundings to the system. And if the temperature of the system were even lower let us say 5 degree Celsius there will still be a temperature well heat transfer from the surroundings to the system. You might notice here that I have written 8 joules per second in the first case and 18 joules per second in the second case. Well these are just examples, but the point I wanted to state here is that because heat is recognized as an energy interaction by virtue of temperature difference temperature difference is the driving force for heat transfer which means that larger the temperature difference the more is the rate of heat transfer. So, larger the temperature difference between a system and its surroundings higher is the temperature well higher is the heat transfer. And which is why in the first case where the system was at 15 degree Celsius and the surroundings was at 25 degree Celsius we had heat transfer of let us say 8 joules per second whereas, in the second case because of the higher temperature differential between the system and the surroundings the rate of heat transfer is higher in the second case as compared to the first. And therefore, the point here is that rate of heat transfer is a very strong function of the temperature difference. The primary reason being heat transfer is basically by virtue of a temperature differential between system and its surroundings or between two different systems. And therefore, the higher the temperature difference or higher the temperature gradient between a system and its surroundings the greater or higher would be the rate of heat transfer. And so, in thermodynamics we would always refer to heat basically meaning heat transfer. So, whenever we refer to the term heat it actually means heat transfer. And as we have seen earlier heat transfer is energy in transit by virtue of a temperature difference. And if in a process there is no heat transfer across the system boundaries then that particular process is known as an adiabatic process that is a process during which there is no heat transfer possible is known as an adiabatic process. And there are different modes of heat transfer or different mechanisms of heat transfer. We shall not go into the details of these modes of heat transfer in this particular course as it is out of the scope of the syllabus. But I guess you would have already heard about these terms that heat transfer mechanisms there are basically three mechanisms of heat transfer. One is known as conduction the other is convection and the third is radiation. So, heat transfer can take place through three different mechanisms conduction convection and radiation. We shall not discuss details of these mechanisms of heat transfer you may refer to any text book on heat transfer for more information on these mechanisms of heat transfer. Now, heat transfer as I mentioned earlier is recognized as an energy interaction between a system and its surroundings only as it crosses the system boundaries that is a system may possess as we commonly refer to a system may have particular amount of heat. But thermodynamically a system is supposed to have had an energy interaction with the surroundings only as the heat which the so called heat which the system has crosses the system boundaries. So, let us look at an example where I shall illustrate this point in little more detail. Now, the system that we are referring to here in this example let us say has a thermal energy of about 5 kilo joules just for an example. So, this is a system boundary as you can see and it is surrounded by a surrounding air. Now, if the energy that is contained within the system crosses the system boundary then that particular energy interaction which the system has had with the surroundings is referred to as heat. So, as long as the system does not interact well as long as the system does not transfer energy with the surroundings that is not thermodynamically referred to as heat. So, heat is considered to have or heat transfer is recognized as an energy interaction only as it crosses the system boundary. Now, if you were to look at this one small example which I would like to illustrate that we have a system here which is bounded by an insulation. So, there is an insulation which is bounding a system and what is contained inside the system it is let us say a candle which is burning. So, a candle is contained within the system boundaries and the system is insulated which means that there cannot be any energy interaction between the system and the surroundings. So, for this particular system in question is there any heat transfer which takes place during this burning process. So, that is one of the questions that you may have and the other question is that is there any change in the internal energy of the system. Now, let us try to analyze these questions a little deeper. So, we have here a candle which is burning within a system volume and the system is insulated. So, because the system is insulated there is no energy interaction which is possible between the system and the surroundings and therefore, obviously there cannot be any heat transfer which can take place between the system and surroundings. So, thermodynamically there is no heat transfer taking place in this process and the second question was is there any change in internal energy. Well, you may wonder that because the candle is burning there should be a change in internal energy of the system. Well, the answer to that question is that there is no change in internal energy as well. The reason is that as we have seen earlier that for a system and the surroundings the net change in energy of that particular process if it is stationary will be equal to the change in internal energy because kinetic energy and potential energy are 0. So, in this case we have a system wherein delta E is equal to delta U. Now, the question was is there any change in delta U? Well, there could be a change in delta U only if there is a change in delta E and the first question which we answered was there is no heat transfer taking place between the system and the surroundings. So, there is no change or net change in energy of the system and the surroundings which means that delta E is equal to 0. And therefore, delta U that is internal energy change will also be equal to 0 which means that for an adiabatic process there is no change in the internal energy of the system as well as there is no heat transfer taking place between the system and the surroundings. Now let us now define the other mode of energy interaction which we had classified or qualified as work. Now, work is any energy interaction which takes place between the system and surroundings other than temperature difference. So, any energy interaction which takes place between this system and the surroundings by virtue of something which is other than temperature difference is classified as work which means that any energy interaction which takes place between a system and its surroundings by virtue of any other property which is not by associated with temperature difference is known as work. And thermodynamically we shall define work in the next slide work is basically the energy transfer associated with the force acting acting through a certain distance. So, if we were to look at work and heat transfer there is a certain sign convention that we follow for heat transfer processes as well as for work. And in thermodynamics heat transfer to a system and work done by a system are usually taken as positive that is we attach a sign to heat transfer and work done heat transfer to a system and work done by a system are taken as positive. And therefore, heat transfer from a system and work done on a system are negative. So, the interaction between the system and the surrounding is illustrated here the two modes for a closed system are heat and work. So, heat transfer to a system let us say Q in and work done by a system that is W out these two are usually taken as positive. And heat transfer from a system and work done on a system that is Q out and W in are usually taken as negative. So, this is a sign convention which we normally following thermodynamics. Now, let us look at both heat and work interactions in little more detail both heat and work as we know now are both energy interactions which are by virtue of energy interaction between the system and the surroundings. So, both are usually referred to as boundary phenomena because these are both energy interaction which take place across the system boundary. And therefore, you also referred to as boundary phenomena and a system can possess energy, but it cannot possess heat or work as we have seen heat or work are energy interactions between system and surroundings. And therefore, they are also referred to as boundary phenomena. Therefore, a system cannot essentially possess or contain heat or work well they can contain energy, but not heat or work. And both system both heat and work are associated with a process and it is not associated with a state and unlike properties heat and work do not have any meaning at a particular state. And therefore, both of these that is heat and work are also known as path functions that is their magnitudes depend upon the path followed during a process. And as it also depends upon the end states, but unlike properties which are point functions both heat and work depend on the path taken during the process as well as the end states. So, you might wonder what are path and point functions. Let us look at what are path and point functions. Well path functions are those functions which depend upon the path of the system as the name suggests. And both all path functions have in exact differentials and these are sometimes designated in different textbooks it is designated in different ways. It is sometimes designated by symbols delta Greek symbol delta or D with a cross. Examples are delta Q or D cross Q or in the case of work it could be delta W or D cross W instead of D Q and D W. But you might also come across some textbooks where it is also referred to as just D Q and D W, but I think it is already implicit that these are path functions. And point functions on the other hand like properties of a system these are exact differentials and they are designated by symbol D. And therefore, change in pressure or differential change in pressure is denoted by D P differential change in volume by D V and D T and so on. So, these are properties of a system and therefore, also referred to as point functions. Now, let us look at an example to explain the properties which are point functions and path functions. Now, in this pressure and volume diagram P V diagram we can see two processes process A and process B taking place between states 1 and 2. So, in the first process that is process A we have change in volume delta V because the states end states are the same in both the processes. The change in volume delta V is equal to 4 meter cube as the initial volume was 1 meter cube and the final volume was 5 meter cube. The delta V change in volume is 4 meter cube for both the processes. But if you look at work which has occurred during process A and process B it will be different basically because from the P V diagram work done during this any process will be the area under the curve in a P V diagram. So, for the first process that is process A, W A will be area under this process A and for the second process W B will be area under process B. So, as you can see W B should be greater than W A and therefore, work is a path function that is it depends upon how the process is carried out and or the path taken by the process unlike properties like volume here. It does not depend does not matter how the process was carried out it depends only on the end states and which means that if you want to integrate volume between states 1 and 2 integral 1 to 2 d V is equal to V 2 minus V 1 because it is an exact differential. Whereas, you cannot integrate 1 to 2 d W because it is not equal to W 2 minus W 1 and the other aspect of property is that if you have a cyclic integral of a property it obviously will be equal to 0. Therefore, properties all properties of a system like volume, temperature, pressure etcetera are point functions whereas, heat and work are path functions. Now, let us define what is meant by work. So, thermodynamically as it is defined work done by a system and its surroundings is basically referred to as a work interaction if there is the sole effect of this interaction can be viewed as raising of a mass through a distance against gravity. That is work done work is said to be done by a system on its surroundings or vice versa if the net effect can be considered to be raising of a particular mass through a certain distance against gravity. So, this is the thermodynamic definition of work. Now, we look at an example to understand what this definition basically means. Now, in this example that I am going to show you we shall consider a system which is having certain interaction with its surroundings and we shall see how we can understand work interaction for this particular system with its surroundings. Now, we have here a system which is bounded within system boundaries. We have an electric motor which is driving a fan and does the system do any work on the surroundings? Well, the motor is driven by a battery which supplies the required power for the motor and it is driving a fan. So, if you were to consider that this system is doing work on the surroundings as per the thermodynamic definition this should reduce to this. That is if we can replace the fan with a pulley it means that we can attach a pulley to instead of a fan to the motor and that can and as the motor rotates this would raise a weight against gravity. And therefore, it satisfies the condition thermodynamic definition of work that the net effect can be considered as raising of a weight against gravity. Therefore, this example which has a system driving a fan definitely does work on the surroundings because we can always replace this fan with a pulley and therefore raise any weight against gravity. And therefore, the system does work on the surroundings as per the thermodynamic definition of work. Now, we shall look at some examples of different work interactions what are the different types of work interactions that are possible between the system and its surroundings. So, there are different ways in which work interactions can be carried out between a system and its surroundings. And we shall look at one of these particular work interaction which is of interest to us as engineers aerospace engineers and that is known as the displacement work. So, we will look at displacement work in lot more detail than the other types of work interactions. So, displacement work is one of the forms or modes of work interaction between the system and the surroundings. The other types of work interactions are for example, electrical work that is if you were to heat a resistor then that is known as electrical work because you can always replace the resistor with a motor and therefore, drive a pulley and raise a weight as we have seen in the previous example. Besides this the other type of work interactions are shaft work that is rotation of a shaft to generate work output or it could be paddle wheel work or spring work or stretching of a liquid film etcetera. So, there are different modes of work interaction which can take place between a system and the surroundings. And one of them as I have mentioned earlier that is displacement work is what we shall be interested in analysis little more. Now, let us illustrate these different modes of work interaction through these examples. So, shaft work that is rotation of a shaft to generate work output as is shown in this example it is a motor car on an automobile which has an engine which generates a shaft work output and that it is that shaft which drives the car the automobile forward and therefore, it generates a work output. The other possible mode of energy interaction or work interaction is spring work example shown here we have a spring which is at rest and in a particular position and if you exert a force on the spring then it expands and gets displaced by a certain distance. So, the work done during this process is referred to as spring work then stretching of a liquid film that is if you were to have a liquid film which is held between the let us say this rigid wire frame and a movable wire. So, there is a surface of film which is formed in between the rigid wire frame and the movable wire. So, as you move the wire it causes stretching of the liquid film here. So, the work done during this process is also one another mode of work interaction electrical work would involve heating of a resistor that is if you have a system which houses a resistor you supply a certain electrical power to the resistor it causes heating of the resistor and. So, there is a work interaction between the system and its surroundings because of heating of this particular resistor. So, these are some examples of different modes of work interaction other than the main form or main mode of work interaction which would we would be interested in that is known as the displacement work. So, displacement work or moving boundary as it is also referred to is of a significant interest to engineers because there are several engineering systems which can be approximated to be operating in the displacement work mode that is they generate work output through the displacement mode. And for example, if you were to look at the engine of an automobile it generates work output because of the movement of the piston during the power stroke of the engine. And therefore, that is displacement work or if you look at steam engines or different pumps many of these pumps and steam engines all operate in the displacement mode that is P times d v mode. So, displacement work as I mentioned there are so many applications engineering applications for displacement work we shall analyze displacement work in little more detail for different types of processes. Now, let us look at what we actually mean by displacement work. Now, in this example I am showing here we have the piston and cylinder arrangement and there is a certain amount of gas which is which is housed within this cylinder volume. And if we were to supply heat to this gas it as we know it would expand and during expansion the piston moves against the atmospheric pressure. And therefore, it exerts a certain force and therefore, this gas does a differential amount of work which is delta w b where b subscript b denotes boundary work. As it does a work it does work equal to delta w b because it forces the piston to move by a differential amount d s. Therefore, delta w b which is the differential work done during this process will be equal to force times the distance. And as we know force is pressure times area because pressure is by definition force per unit area. Therefore, force can be expressed as pressure into area. And as we are also aware that area times this distance will be the volume that the piston has moved or displaced during this process. Therefore, we can replace a times d s by d v. Therefore, the delta w b that is delta work done during this process is equal to p times d v or if you are looking at work done from state 1 to state 2 w b will be integral of p times d v. So, this is why it is known the displacement work is also referred to as p d v work that is pressure times differential volume work p d v work. Now, the same process we can explain in terms of the p v diagram as well. Now, in this p v diagram we can we have the same piston cylinder arrangement here. And as we supply energy to the cylinder the piston moves generating work output that is the process would would take place between states 1 and 2. And this is an expansion process and so the process path is indicated here. This is the process path for this particular process. And if you were to look at one small differential strip in on this process path then the area of that differential strip will be equal to pressure average pressure during this process times d v. And therefore, area is equal to integral d a which is integral p d v. And therefore, area under the curve on a p v diagram will be equal in magnitude to the work done during this quasi static or quasi equilibrium process which could be either a compression process or it could be an expansion process. And it is basically for a closed system. Therefore, area under the curve in a p v diagram should be equal to the work done during this process which obviously is quasi equilibrium or quasi static. And the process may be either compression process or it could be an expansion process. Therefore, if we if we can plot the pressure versus volume diagram for a particular process we can actually calculate or determine the work done during the process simply by measuring the area under the p v diagram. And therefore, for any work interaction process a p v diagram plays a very significant role in analysis of work interaction during a particular process. So, we shall be using p v diagram very often in thermodynamic analysis. And similar to p v diagram we also have what is known as temperature entropy diagram which we shall see in detail later on that is T s diagram. T s diagram also plays a significant role in thermodynamic analysis of engineering systems. Now displacement work as I mentioned because work is a path function it depends upon the path taken by the process and not just the end state. It depends on the end states, but also it depends upon the path taken during the process. Therefore, if you were to look at states 1 and 2 the infinite number of possibilities of carrying out a process between states 1 and 2. The properties at states 1 and 2 remain unchanged, but you could do the process in different ways. And depending upon how you do the process the work done during the process will change. That is if you can do this process by a b and c the work done during each of these process will be different. And as we now know the work done is the area under the curve. And therefore, process a work done during process c will be the least because the area under this curve is the lowest followed by b. And the highest work done would be done during process a because area under this particular process is the highest. Therefore, just an example shown here W a could be let us say 12 kilo joules W b 10 W c is 7 kilo joules and so on. Therefore, the work done during a process depends upon the path as well as the end states. And the net work during a cycle is basically the difference between the work done by the system and work done on the system. That is if you were to consider this as a cycle that is the process starts at let us say state 1 and takes path a and reaches state 2 and then takes path b to come back to state 1 again. The net work done during this process will be area between the curve that is W net will be equal to area under a which is work done by the system. And area minus area under b that is work done on the system which is equal to W net. So, W net will be equal to W a minus W b that is the net work done during this particular cycle. So, net work done during a cycle will be the difference between work done on the by the system and work done on the system. We shall now analyze displacement work done during different processes. So, you can carry out the process in different ways. It could be either a constant pressure process, it could be a constant volume process or it could be a process wherein P v product P v is a constant which happens to be an isothermal process because as per state equation P v is equal to m r t. And therefore, if P v is constant it means that temperature is a constant. So, an isothermal process wherein P v is constant or it could be what is known as a polytropic process wherein we have product P times v raise to n is a constant where n is a number which can depend upon the type of process and that is known as a polytropic process. So, we shall now calculate the work done during these different processes. A constant pressure process, a constant volume process and then we shall consider a polytropic process. P v is equal to constant is a subset of the polytropic process. Now, let us first look at a constant pressure process wherein the pressure remains constant the volume keeps changing during the process. So, if you were to look at the P v diagram for such a process wherein P v is well pressure is constant this process takes place between states 1 and 2. Since pressure is a constant you can see that P 1 is equal to P 2. So, what is the net work done during this process it is basically the area under this curve and how and it is very easy to find the area under this curve because it is just the pressure as it is constant P times v 2 minus v 1 which also comes from integral v 1 to v 2 P d v.  So, work done during a constant pressure process is the product of the pressure times the difference in the volume during the process.  Now, what happens if the volume was constant? So, if you have a process where the volume is constant that is it is a closed system and the volume is also constant, but the pressure can change is there any work done during this process. Now, since v is equal to 0 if you were to integrate P d v between states v 1 and v 2 since v 1 and v 2 are the same in this particular process the work done will be 0 because there is no change in volume of the system and therefore, for a constant volume process the net work done will be equal to 0. So, there is no work done during a constant volume process. Let us look at a polytropic process that is a process in which P times v raise to n is a constant where n can take different values 0 1 2 3 anything. So, we have here on a P v diagram different process are shown here n equal to 1 n equal to 2 n equal to 3 and the limits of this particular process are n equal to 0 when n equal to 0 what happens is that you will have a constant pressure process. We have already seen what is the work done for a constant pressure process which is equal to pressure times the difference in the volumes and if n was equal to infinity then you get volume is equal to constant where in the work done will be equal to 0 because area under the curve is 0. Now for a P v raise to n process work done is integral 1 to 2 P dv which is equal to C times v raise to minus n times dv because P v raise to n is constant let us say the constant is C. So, P v raise to n is equal to C. So, we can replace P by C times v raise to minus n. Now, we also know that since P v raise to n is constant P 1 v 1 raise to n is equal to P 2 v 2 raise to n is equal to C and so if we were to substitute these values into the work equation here that is for if you were to replace v in terms of the pressures what we would get is work done from state 1 to 2 will be C times v 2 raise to minus n plus 1 minus v 1 raise to minus n plus 1 divided by minus n plus 1.  Therefore, work done during polytropic process is basically equal to the product of P 2 v 2 minus P 1 v 1 divided by 1 minus n. So, suppose n was equal to 2 then the work done during this particular polytropic process will be equal to basically depends upon the properties at the n states P 2 v 2 minus P 1 v 1 by 1 minus 2 and so on. So, you can actually calculate the work done during a polytropic process if you know the n states as well as the exponent of the polytropic process. So, we shall see later on that when n is equal to 1.4 where 1.4 raise to n is equal to 4 for normal temperatures is also referred is also equal to the ratio of the specific heats. In such a process we usually referred to this process as P v raise to gamma is equal to a constant where gamma is the ratio of the specific heats C p divided by C v. So, this process we shall see in detail in later lectures. Now, from this particular polytropic process if you were to assign different values of n you can calculate the work done during these different processes and as a subset of this process would be n equal to 1 where in P v is a constant. So, when for P v is equal to constant you can actually integrate we obviously need to integrate P d v for between states 1 and 2. So, if you look at this particular equation if you substitute n equal to 1 then that is not the right way to do it you will still have to go back and integrate for the work equation substituting for in the same way as we did for this case where P v is equal to C and so on and the work equation will come out to be P 1 v 1 log v 2 by v 1. So, I leave that as an exercise for you to calculate the work done during a P v is equal to constant process. So, let me now recap what we have discussed during this particular lecture. We started the lecture by defining what is known as specific heat for a process and we saw that the specific heat is basically the energy required to raise the temperature of a unit mass of a substance by unit degree rise in temperature. And there are two different types of specific heat specific heat at constant pressure and specific heat at constant volume. Subsequently, we discussed about energy interaction modes between a system and its surroundings for a closed system. And for a closed system there are two modes of energy interaction heat transfer and work. And we discussed about heat transfer the meaning of heat transfer basically the thermodynamic meaning of heat transfer and also mentioned about different modes of heat transfer. We discussed about work in lot more detail. We defined thermodynamic definition of work and also the different types of work interactions possible between a system and surroundings. And then we also discussed the displacement work that is PDV work in lot more detail. We also calculated work required for different displacement processes, a constant pressure process, constant volume process and a polytropic process. And somewhere in between the lecture we also discussed about path and point functions. Basically path functions are those which depend upon the path of a particular process as well as the end states. And point functions depend only on the end states. All properties of a system are point functions, heat and work are path functions. So, this is what we discussed in today's lecture. And in the next lecture what we shall do is to solve some problems based on what we have discussed during lectures 4, 5 and 6. Primarily we shall solve some problems related to calculation of work done during different types of processes. So, we shall solve these problems during the next lecture.


This is covering the spread part of the Fandall podcast network a Potential Super Bowl preview is coming up in week 16. We've got the Baltimore Ravens heading to San Francisco to take on the 49ers We're gonna break down that game and all other week 16 key games by talking to Dr. Ed Feng Getting you ready to see what his number say about those key games including Ravens versus 49ers and other bets He likes for this week at Fandall sportsbook This is covering the spread right here on the Fandall podcast network and Fandall research My name is Jim Sonnis I am a managing editor of digital media for Fandall research joined here as I am every Thursday by Dr. Ed Feng You can find his work at the power link comm and check him out on Twitter at the power like Ed Thrilling slate of games coming up for this week. How you doing today? I'm doing really well. I'm looking forward to another weekend with a lot of NFL games spaced out very nicely Start tonight on Thursday night and then have all the Saturday games have multiple Monday games Which is which is pretty awesome. Yeah, and the Thursday game this week is actually pretty good Ram Saints I'm intrigued by that game just because I've been Higher than I should be on the Saints most of this year that spread is tied into three and a half Which makes me feel a bit better about that game and you know being high on the Saints And they're a miserable team to watch if you ever bet on them Like if you ever bet the Saints just don't watch the game like that's not it's not worth it Believe me But it should be a fun one Thursday and then a fun one to bookend things on Monday as well Ravens versus 49ers. So honestly like it's not just that they're spaced out well I but it's also good games in most time slots, too Right. I mean especially with the the end on Monday night is gonna be particularly good Christmas Day Yeah, absolutely breakdown that game later on and get you ready for all games across week 16 Throughout the show for today But first a reminder to make sure you're subscribed to covering this spread wherever you get your podcasts are breakdown of that Thursday night game Between the Rams and Saints is already up via Tom Vecchio prime time Tom breaking down top props for that game That isn't the covering the spread podcast feed and over on a fan dual TV plus No show on Friday for this week because of the holidays and then no show Monday as well So it's gonna be our only preview of week 16 because we're taking some time off for the holidays back with you on Tuesday To keep your firstly look NFL week 17 That is with us next week on Wednesday and Thursday We'll talk the college football semi-finals coming up then so make sure subscribe to covering the spread wherever you get your podcast And if you like what you hear leave us a five-star rating on Apple podcast or over on Spotify score early This NFL season with fan dual America's number one sports book right now new customers get $150 and bonus bets with any winning $5 moneyline bet That's a hundred fifty bucks if your team wins if you've been thinking about joining fan dual There is no better time to get in on the action the app is so easy to use There is a wide range of betting options including spreads player props totals and more so there's a fan dual a kickoff The NFL season fan dual official partner of the NFL must be 21 plus and president select states Fan dual is offering online sports waging in Kansas under an agreement with Kansas Star Casino LLC first online real mini wager only $5 pregame moneyline wager required $10 first deposit required bonus issued is now a drop of bonus bets that expire seven dates after a seat See terms at sportsbook.fan dual calm gambling problem call 1 800 gambler or visit fan dual calm slash RG in Colorado Iowa, Michigan New Jersey, Ohio, Pennsylvania, Illinois, Kentucky, Tennessee and Virginia Call 1 800 next step the text except a five three three four two in Arizona one eight eight seventy nine 7777 or for the ccpg.org slash chat Connecticut 1809 with an Indiana one hundred five two two forty seven hundred visit ksgaminghealth.com in Kansas 1877 770 stop in Louisiana visit MD gambling health at Oregon, Maryland 1 800 gambler.net in West Virginia 1 800 five two two forty seven hundred in Wyoming. Hope is here visit gambling helpline ma.org or calling hundred three two seven 5050 for twenty four seven supportive Massachusetts or call one eight seven seventy open y or text open y in New York Now before you get into the games. I want to talk about Some perceptions we've had of a couple of teams this year specifically Dallas in Miami who happened to play each other this week But how they can't beat this super stiff competition I think that was kind of strengthened this week with the bills Throttling the Cowboys up in Buffalo both you and I run numbers that account for opposition so My baseline assumption is that our numbers properly account for a strength of schedule and stuff like that, but Do you think those narratives about some teams struggling against elite level of competition? Are accurate or is it just a narrative that stems from variance and small samples I think it stems from so small sample size. I've definitely heard some of these ideas from people that I really respect and are better sports better than me, but I still don't really believe I look back at these teams and the one commonality they seem to have is they both really struggled Against Buffalo, which is the team we were writing off because of their record Not me, but some people were writing off because of the record a couple weeks ago We know Buffalo is a very good team and it just seems really odd to me that you know Yeah, so Dallas can't play against the lead teams and Buffalo is the lead team, but they weren't a couple weeks ago Because of the turnovers. It doesn't make a ton of sense to me. So, um Yeah, I don't buy it I don't either and I think that a lot of it stems from like For dallas specifically I think comes down to the elite teams are just bad matchups for them And that's just coincidence. It's not they can't beat elite teams It was that the bills are a very good rushing offense or did in that game And then the other one they ping on the cowboys is the 49ers and like that's also an elite rushing offense And like that's the kind of situation where dallas can really struggle. So Like if they're facing I don't know like if you put them up against the chiefs I think dallas would play very well in that game because the rushing offense for the chiefs is pretty good But it's not quite that level and it's like it's kind of the same thing we saw with like those Packers defense is a couple years ago where like they were just really bad against the run And it kind of like nullified everything that they had So I think for me it's more so about just poor meshing with the cowboys with the With the with the dolphins we've even seen them face a lot of great teams recently Like they've had only a couple matchups against top 10 defenses so far this year and spend the jets a couple of times They're often played pretty well in both those games. It was basically just that that bills game to an extent the chiefs game, but like That was kind of funky as well. So i'm on board of the ued. I think that it's more soge variance and It's a small sample sport, but it's even smaller once you whittle it down to Just looking at the elite teams, especially once you have some like selection buys Which teams you deem to be elite in which ones you don't? Yeah, no, absolutely. Um, and just just to note about dallas like dak has gone through these interesting two seasons where you know in terms of The fraction of times he put the balls in major situations has been about the same um, but picks last year and has had really Just not a lot this year. So um, I think ball flows. Sorry dallas is uh, I guess Hope of your dallas fan is that you know, he continues to get lucky with uh, with uh, with with the turnovers I think that dak last and he might not dak last year is what's happened in my home this year Where it's a lot of balls going off receivers hands and like Maybe it's just because the receivers are trash, but it's also it's probably just bad luck So I think that definitely some bad luck or some good luck for dak this year And uh, we'll see how long it continues Absolutely, so we'll talk about that uh dolphins versus cowboys game here In just a bit, but let's begin things by talking about pretty fun game in the early slot on sunday That is the lions at the vikings or right now the lions are three point favorites total in this game has gone up a half point to 47 The lions at are still even money to make the playoffs right now despite some Really rough games recently pretty critical game here as they take on the lions Do they have the juice to keep pace here with this lions team keep this game close and potentially win it or no We shall see When I was watching minnesota and since then I this past week and I was thinking about oh, I mean I guess and then the detroit game right after that I really thought I uh, I'd be betting detroit in this spot The idea is detroit definitely has an elite pass offense question questionable on defense, but minnesota You know, I thought that game was a little bit deceiving in in terms of uh, what we saw from nick mullins There was a pick six that now got negated by a penalty I thought there was another Ball that he threw right into the hands of his insane receiver that was dropped that also could have gone a long way The other direction the data actually doesn't agree with that because it says he had Too bad balls and they both turned into interceptions So i'm not exactly sure what happened with that second one because I do think that was a legit play Um, but then you know when you go back and look at the data It's like well, I mean mullins actually had 61 passing success rate, which is ridiculously good Certainly showed all There were certainly some good things for nick mullins in there as well And traditionally he hasn't been awful in terms of putting the ball in dangerous positions Let's not give detroit too much credit for beating demver We talked last week about how demver is a fraud And a complete fraud and and don't get fooled by the fact they're almost seven point favorite against Bailey zappy this week So, you know, I have detroit by about 2.6 points my model Not showing any value here as much as I'd like to bet detroit on the road I do think they'd get this done on The road, but probably not a lot of value You know gun to head you I would certainly lean towards detroit because I do think that is the right way to go But um, you know, I mean on looking at the data on mullins. It was better than What I saw from then in the game Yeah, he uh, the way I've described nick mullins week is that he is Josh allen minus the things that make josh allen good Like without being like athletic like he's got chaos josh allen genes But then doesn't have like a good arm. It isn't fast. Um, and like there you go. Okay it's like It's frustrating to watch because like, yeah, like I looked at the efficiency numbers too and like they were good they were they were really good like he said but like I thought he's gonna get benched in that game for jaren hall at one point. Uh, like it was it was that bad And I think that if it weren't for the lions defense or past defense being as bad as it would be Maybe I would be all the lions here as well I've got the lions minus three and a half personally So the the market right between our two models sitting at three right now I think that's appropriate So I agree with that the one thing that I do see in this game is potentially an under Now it's into 47. I have 44 and a half as the total here Vikings defense has played pretty well. The lions are okay being a bit run heavy In the spots where they can run so I could see an under potentially playing through in this game But as far as the side goes, I think the market's pretty spot on here But I think the under isn't shrinking at 47 Given 47 is a key number. You're gonna push on a key number right now I think that could be the way to play this game if you were looking for action on it Um, but like I think the other thing yet is uh, yeah, cj. Gardner johnson Maybe back he's back at practice. I know For wednesday. So maybe he's back for this game. That'd be a big lift for this This lion's secondary because ed they need it. They need that all the help they can get back there right now Well, I mean honestly the personnel is a heck of a lot better than it's been the past these seasons still Yes, I do think I do think I expect a little bit more You know, I mean they were they were NFL average for a while this season I do think there's a reasonable hope they get back there But obviously having uh, all hands on deck with uh, would certainly help And I think a lot of the reason they've dipped is the injuries. So getting guys like cj. Gardner johnson back would help Quite a bit there Let's talk now about that matchup between the cowboys and the dolphins right now It is the dolphins minus one and a half of fandom sports book total in this game It's 50 and a half uh over is minus 105 on that that total has come down a point throughout the day for today And the cowboys. Yeah, they did flop last week But they had been playing a really good football up to that point now You talked a lot about this dolphin's defense and how good they've been since jaylon ramsey came back So Do you see the cowboys bouncing back here or does that dolphins defense continue to impress? Right. I mean, I I don't see a ton of value. I have miami by two points in this game I essentially am rating these two teams about the same. I think that makes a lot of sense Let's talk about the miami defense. Um, I think they were looking better And whatever numbers I was citing last week One of the things that has changed in my world is that uh, now I apply my strength to schedule algorithm But I actually make it specific to the quarterback So because there's a difference between daniel jones and and tommy devito When when you do that Miami's actually 29th in in my passing success rate on defense. That's not good Uh, you can look at a couple reasons. Uh, they weren't good against tennessee and will love us so And then, you know, they faced wilson, but they also got the benefit of uh facing tim boil and that previous matchup And as bad as he was, you know You don't look good when you face him boil, right? Like you don't you don't get a lot of credit for that So I haven't broken it down into early late season. I think that would be a little bit different, but I do think you kind of have to dock them. Yes, they look good and and yes, it's been better But you know, let's let's still keep in mind who they've had to play um So we'll see. I mean, obviously, Miami's offense is still great and and they're really, uh, you know, I mean These are two really good teams. I think it's going to be a great game. Uh, really don't have opinion or bet on it Um, but uh, yeah, let's let's hold off on thinking the Miami defense is is where where we think it might be Yeah, the quarter of x a face recently are aiden o'Connell They faced there was someone in there who was actually fine if I recall But then they faced tim boil like you said they faced will levis and levis kind of shredded them, especially late in that game He shredded them. Yeah, that's not good, right? And then they faced uh, zack wilson who got concussed I think i'm like the second play of the game He stayed in for the rest of the half but like I think he had a cast like right away And then it was trevor simian and I I love trevor simian the human being Not a huge fan of trevor simian the quarterback um so like They faced a lot of really bad quarterback play recently and once you account for that like They haven't really done that well against like competent teams other than sam howell sam howell was in the mix there too Uh, that was the other quarterback of the stretch. So it's been aiden o'Connell tim boil Sam howell will levis then a combo of concussed to zack wilson and trevor simian like Yeah, that's not a whole lot I had a I had a good one for my numbers this weekend jim because I actually wrote about green bay Steve fence and how they they went from kind of bottom-ish mid to like orc in the nfl when you when you did this analysis Yeah, uh, and one of the big reasons is like Actually, no, I didn't end up throwing out the game with brett rippin They they got the rams with brett rippin instead of matt stafford and that you know that kind of matters Kind of makes a difference a little bit and uh, so that was a good one because they they instantly got shredded by by Bay They also had, uh, you know looking back at it Tommy divvido by far had his outlier performance against Green Bay, which you can say, oh, maybe he just played that one good game But then, you know, or maybe just green Bay's defense is bad and when you trade away with jewel douglas and jair alexander is out doesn't help at all. So Yeah, so anyways, I got you know got fortunate that I wrote about green bay in the newsletter last week and You know saying some of the things about in miami. We'll see what happens against else Yeah, it's a lot, uh, you know It could be that the the packers defense is bad or that baker mayfield's best quarterback in history of football You choose, you know, it's one of the others. So baker baker mayfield. I think he has shown that he's you know Perfectly adequate. He should be a starter nfl as a quarterback on a good year and he's having a good year He's not going to bring you to this.  Yeah, you know, I mean if you give him mike evans and chris godwin Baker can be fine like and that's true for a lot of quarterbacks, but like, you know, it's still something So give him a good infrastructure If he's realistic about a salary, you know, and they can actually support him with good players Then he can be fine. So, uh, it was fun to watch him shred a bit on Sunday while cleveland's turning to joe flacco in order to try to turn their season around Alrighty Ed, let's talk about that banger to finish things off on monday night The ravens at the 49ers right now the 49ers are five and a half point favorites total in this game is 46 and a half and It's a decently large spread You know Given how good the ravens are but I show value in the 49ers here Now I saw your tweets a couple days ago saying that you actually show value on the ravens So I want to talk I want you to talk me through What you're seeing here is the market overselling how good the niners are or the ravens just like Sneakily very very good and being underrated here. What's your view of this game ravens at 49ers? right, I mean, so, uh, I I think those were my public numbers that you were talking about but You know, I I tend to point out a prediction where my public numbers are pretty close to my best numbers And so I have san francisco by four in this game. I really like baltimore as a football team I really would like to bet them plus five and a half but Zay flowers and and obj aren't practicing. They're questionable mark andrews is out Cluster, I mean that has to be worth at least a couple points that if all three of them are out So, you know, there's probably a world in which flowers and obj Are 100 by monday night and and I would bet this game Uh, but I mean this this really should be a good game. I mean, uh baltimore's defense has passed Second in my passing success rate adjusted for Opponent you can see how tough they were Against jacksonville. Uh, that was last week, right? So anyways baltimore's uh baltimore's uh past events is really good. I really like both these teams. I actually have a future on, uh, uh, san francisco baltimore super bowl And the reason I bet this is is not because I actually went and calculated some numbers But uh, the fact that my son came up to me and with a youtube theory that the teams that make the super bowl Have the same colors as in the super bowl logo So he's like, you know, that means baltimore and san francisco are going to be playing in the super bowl And this was at least a month ago where and it was less obvious That these were the two best teams at least how based on how these are clearly the two best teams based on how they play this year Um, so he's like, yeah, yeah, can we put some money on that and uh, I was like, sure I think they're both really good football teams And so now my son is like a rabid baltimore and yeah, and uh, san francisco fan, which is which is hilarious Does he get a percentage of that wins? He does. Okay, good. He does So say i'll be his agent if I need to be like to to enforce to make sure that he gets proper credit for this Yep, no, no, no, no. He will uh, yeah, he's he's pretty pumped Okay, well, that's awesome. I have I have a ravens plus nine fifty super bowl ticket that I feel pretty good about right now I think they're plus five fifty last time I checked so Do you like that feel good about that as far as the injuries go for the ravens Uh beckham did not practice again on thursday zay flowers was at practice But then also the left tackle ronnie stanley is in concussion protocol He was at practice but in a red non contact jersey I assume that means he'll be limited on thursday if he gets in a limited practice on thursday I tend to assume he'll be cleared by monday. That's kind of in the progression is like You get in two days of practice and then you can be cleared It's been very odd though because like my like if i'm putting in Injury expectations on a monday for the upcoming games I've been assuming guys in concussion protocol will not play almost this entire year But ever since that week where brock pretty clear cleared quickly We've seen a lot of players get through protocol a lot faster than they have before and it's messing up my process So I'm annoyed by that honestly because like if like stanley playing as part of why I'd value the niners Um, it wasn't the entire reason or a stanley missing. I thought right if you were gonna be out I would show value there because it's a big ding to the ravens offense not have them Lamar sacrate is 1.5 percentage points higher when stanley is off the field versus when he's on you're facing nick bosa All these like really good pass rushers so I'm a bit annoyed by that. I might need to tweak my process as far as guys Uh cush protocol michael pittman the same thing.  I wish they would just keep things consistent. Uh, so I can Make these projections on a monday, but It does help. I do like the over in this game too. It's gone up a point It's uh 46 and a half right now over is minus 115 the one issue with that is part of that is because I show value in the spread and If I'm if I have the Niners covering five and a half that implies more points are scored So it makes sense that I'd show value in the total over as well And if if I'm a bit overselling Uh, the Niners here that would imply that maybe a bit too high in the total too But I think 46 and a half the over there is pretty enticing Do you like the ravens enough to take the five and a half or The concerns about beckham flowers stanley and the cluster injuries worry you there Yeah, I mean, I'm gonna wait if this number is still five and a half and flowers and obj are going and stanley's going Yeah, I'll bet that. Okay. It's five and a half minus 115 right now. That was minus 105 Earlier this week, so it has been looks like there's been some action on the raven side Uh, I fanned a sports book but still at five and a half as of right now But should be a delightful game to watch on monday any other spots where you see value across week number 16 ed Yeah, I wanted to talk about Um Cleveland of houston and we have to go back to when we expected cj stroud to come off the concussion protocol Uh, I sent this out to members, but it the number, you know, it was houston minus two and a half at home And that meant you essentially had to rate these two teams equal When uh, so I've thrown out the prior on houston, so I don't I don't even consider What they've done because they've they've just been a lot better than Then we expected this preseason Even when you do that like I actually have houston right at nfl average based on data from the current season based on market so They've you know, the offense has been good No, it's been very good for having to work your quarterback, but it is um, you know, it's not an elite offense yet You know when you look over the whole span of the season You know, I have the better than nfl average Um, I have the defense has gotten a lot better But overall you have to rate them at nfl average now when you look at cleveland again I'm thinking about now now i'm telling you about the calculations that are specific to joe flacco And he's actually been pretty good Uh, which is a little bit of a surprise for the 38 year old who couldn't do crap For the new york jets last week, but you know, I mean we're taking a data-graced approach And like it's not like, you know, I mean you look at this You know almost 44 passing success rate against chicago defense that had looked pretty good in the weeks before that that has gotten healthy in the secondary and so I combine um, so kind of the new model that when when when you have a quarterback that isn't uh, who you expect at the start of the season is You know the quarterback adjusted passing success rate yards for past attempts and then um, the market model is specific to quarterbacks, too Right, so it'll tell you exactly what the market thinks about cleveland Uh, I actually have them as four points better than nfl average with flacco Uh, if you think that's too much, I probably agree with you but You know cleveland is better than nfl average and you know If you think about it like they have the best defense in the nfl No one's really going to argue about that to get them down to nfl average You really have to think flacco in the offense is quite significantly below nfl average to get to a point where you know You want houston You can make that number houston minus two and a half right and I just couldn't get there You know my model actually liked cleveland favored with cj stroud And so clearly got a little bit lucky here. Uh strouts out looks like case games going to play You know the numbers move to cleveland minus two and a half I don't know quite where to to put the number now You know, I think case games are pretty good quarterback. Uh in terms of the realm of nfl backups um, so But but anyways earlier in this week, this this was great. Um, and I thought the analysis was solid, but uh You know part of that was like, you know, he stroud might not play And so there is a probability that this is going to come screaming towards cleveland and it did Um, so obviously not available anymore, but again, I wanted to talk about Yeah, I think that that game is super interesting just because I liked it's similar to you ed You liked the brown side When stroud is projected to go I like the under when brought when stroud is projected to go because this brown's defense has been very good They've been way less good on the road than they have been at home Like they've been a very good defense once you adjust for schedule and things like that So at 42 and a half I took the under there And then now when you take stroud out, I've got this total at like 34 And it's a 40 and a half right now. Uh minus one 20 on the under So it's definitely, you know still there, but like I'm kind of that's I think that's the thing that surprised me the most This total has not come down more I know The browns have been very past heavy with flacco in addition to having that high success rate as you alluded to Like they've been very past heavy, uh more past heaviness is conducive to overs and Houston's past defense is pretty bad, but like still It seems high to have this at 40 and a half if we have case keenum starting for the Texans in this game Yeah, I mean we'll see how it goes. Uh Yeah, for sure Absolutely, okay Well, that's all that we have here for today on covering the spread But like I said, it should be a very fun week in the nfl next week three shows Tuesday with ryan williams wednesday with ed and Thursday with ed as well talking college football to get you set for the semifinals on wednesday and nfl week 17 Coming at you on thursday to get those shows as they are posted Make sure you're subscribed to covering the spread wherever you get your podcast You can also find us on the fandall youtube page And fandall tv plus ed. What is going on for you this week at the powerink? Yeah, check out my free sports betting email newsletter. You can get that at the powerink.com 5 no, it's saturday, uh try to uh get some bets from from other people That I think are sharp was fortunate enough to have two winners Last week from from ryan newton over at four for four and then cleat da who Is pretty well respected quantitative better So yeah, check that out if you're looking for action on any given weekend. Uh, check it out at the powerink.com All right, you can find ed on twitter at the powerink ed happy holidays to you and happy holidays to our listeners out there as well Appreciate all of you for tuning in you can find me on twitter at jim sonnis You can find me on threads at jim dot sonnis You can find fandall research on twitter at fandall research have a fantastic weekend everyone Be happy be safe be healthy and we'll talk to you once again next week on tuesday to get you ready for week 17 This has been covering the spread right here on the fandall podcast network


diesel bad re-review. Hey what's up guys it's Josh here today I wanted to do a little review on this diesel bad technically it's kind of like a re-review diesel has always been a freggers company that I actually really really like but actually a lot of people don't really like diesel is probably one of the least hyped freggers companies out there except for maybe only the brave the other ones they really have a fuel for life and bad and most of the time people really really don't like those for some reason but I actually really liked fuel for life when I first smelled it in 2009 since then there has been a lot of fragrances that come out that are probably I would say I might like a little bit more than that but I really did like fuel for life back in the day diesel seems to make these kind of like masculine a little bit dirty a little bit sexy fragrances generally towards the younger crowd like almost all the times I smell the fragrances it's kind of like in that Invictus E 1 million style realm with a little bit more of a dirty quality and it seems like they try to do more unique stuff or more unique fragrance than something like Invictus or 1 million but at the same time they go even farther away from normal fragrances which I think some people don't like we got a lot of notes here let's ramble them off lavender bergamot cardamom violet leaf caviar oris root sage woody notes tobacco tonka bean and broxen and patchouli there's really not very many prominent notes that you've smelled before that's going to be actually in the cons but there really isn't too many fragrance notes you got Invictus with that really noticeable mandarin orange you got something like 1 million with that really distinct cinnamon note things that you have smelled before this fragrance really does not smell very conventional personally I get a tiny bit of bergamot on the top I've never really smelled caviar I've never really ate caviar but although it is very synthetic I do see a little bit where the caviar is coming from I do smell a little bit of this age I smell the woody notes a hair of tobacco and a hair of embroxen but again these are just little bits of nuances this fragrance really doesn't smell overly like one of these notes for me personally what this kind of reminds me of personally is Abercrombin Fitch fierce mixed with a little bit of like something closer to ch men privet and again it's not a hundred percent like half fierce half ch men privet it's almost got some solid elements of fierce in my opinion what makes this smell like fierce is the combination of the sage and embroxen new versions of fierce I think a feature a lot of sage and the sage actually kind of recreates the classic smell a little bit which is crazy because I don't think the original had sage but the sage and embroxen combo give it this this transparency and fierce has the iso e super for me I find embroxen and iso e super to be kind of in the same realm they kind of have this hormonal sexy quality that's used to spice up fragrances so I do smell that and then what I think of what would smell like ch men privet is probably a little bit of the tobacco tonka bean a little bit of the woody notes it is a little bit of a darker spell but again it's not a hundred percent like those and I probably would prefer the classic fierce ch men probably to this one just because I those are some of my favorite fragrances of all time this one is very nice I think I wore this for about five or six days testing at maybe seven surprise that I didn't spray it all I think it's like a one ounce and I actually sprayed up quite a bit of this and it's still like well over halfway so really really enjoyed this stuff guys for what it does I'll get more into the cons coming up soon I know there is some cons I know people don't like it let's start off with the pros what I really like about this it's different it's daring and it has a good presentation I really like the presentation of this guys I like the see-through a bit of it I like all the ad campaigns I like the feel of it I've never really had a fragrance that has this exact kind of feel I just really like the presentation I really do like they're trying to do something different and way out there whether or not you actually really like it depends on the person a little bit but I do really appreciate what they try to do they try to give us something that's not super safe and super normal something like why is so why just super safe all these other ones just super super safe and likeable and it's great because it's going to be likeable I get it but I really want you to try to do a new fragrance I really really appreciate that my opinion it's a very good smell and good compliments for the right situation I would say maybe about a third of the situations this is very very very good but again there's a lot of people in a lot of situations that this is not for I could see this being like an everyday scent of somebody who's in there like 20 25 maybe getting up closer to 30 this isn't really something that's overly super clean that you would wear like dressed up with a suit and tie just don't see it it's got a little more casualness to it also in my opinion I could see somebody wearing this for work but again a certain personality who would wear this every day but generally not for work or anything like that let's go into the cons the cons is that I have only really like two is that it's very very synthetic now there's a lot of fragrances that are very synthetic but even compared to likes I would say this is kind of in that Invictus and one million style smell and again those fragrances have some notes that you have smelled before so it has some familiarity and I feel like it doesn't smell as synthetic because you can actually smell those real notes in there this one really doesn't smell like anything in nature most of these notes don't really come through so it does come off pretty synthetic I see that certain people are really just not going to like this fragrance I totally get where they're coming from and like I said it's not like for dressing up I wouldn't say this is pure over 40 maybe you you would like this fragrance but I wouldn't I will really suggest it for somebody you know older but I feel like it does have its own niche and you know I think a lot of younger guys are into colognes and you know want just a little something to spritz themselves up and I feel like this is a little bit it does something different and I definitely recommend trying it before you buy it but I can almost guarantee you there's a certain amount of people watching this video that really really do like this fragrance as well but again it's probably about a third of the people a third of the time but when you do wear this at the right time I think it will be very great and I do see it getting compliments so finally guys for the smell rating this is going to be completely based on what you think of fragrances by yourself I could see you somebody really really like in this one are really really dislike in this one so I'm going to give it a 7.5 to an 8 to me I think somebody would like this more than an 8 and I think people would like this a lot less than a 7.5 so I'm kind of going in the middle likeability again the same exact thing there's certain people who are going to really really like this fragrance there's certain times you're going to wear this and it's going to be very very sexy and very good that definitely is not all the time and this is a fragrance that a lot of people have smelled and a lot of people did not like although I think it's a little bit above average it's not the greatest thing I've ever smelled but I really do enjoy it so 7.5 to an 8 for likeability I think that is fair I wrote down 7.5 to an 8 for longevity of projection but I'll probably go with the solid 7.5 and if you've been watching my recent videos sometimes a fragrance that has an average projection I would give a 6.5 to a 7 so this is a 7.5 it's really noticeable it's there but then it also you know if you're going into a place with a lot of smells or you have a lot of wind it isn't like overkill by any means but it's also not really that weak so I'm going to give it a solid 7.5 I recommend this for a specific kind of person I definitely recommend trying it out if you like those kind of in-your-face sexier youthful kind of fragrances a little bit dirty this fragrance could be for you if you're somebody who likes overly clean stuff overly mature stuff you know you're in your 40s and you have a great job making a lot of money probably not for you this is really is like a love it or hate it style fragrance and I'm closer to loving it than hating it but I totally 100% see where people would not like this one however I'd really do I think the diesel bad they have like an extreme version or an intense version and that version smelled a little bit more like orange to me if you guys want me to review that let me know also any other cheapy suggestions or designer suggestions let me know which fragrances I should pick up next we're on the road of 25,000 subscribers we are really really close to being there and I couldn't do without any of you guys hope you guys are the best I'm having a great day out here hopefully having a great day at home see you all in the next video peace there's a lot of fragrances that are