today. Oh, pretty good today. Did physical therapy work with you this morning? Yes, they did. Are you having any pain right now, Jane? No. Good. Do you feel like your pain is pretty well managed here? Yeah, pretty much. I was just going to check your vital signs. Is that okay before you go to bed? Did you get a chance to go outside today? So another day of physical therapy, one more day closer to home. That's right. They become like family members to you. You get to see the impact that you have in people's lives. Just the most fulfilling thing is to know that at the end of the day you've helped somebody. It's important to me that they know that they're in secure hands, that they're here knowing I'm going to be taking care of everything's going to be okay.


Now, let's look at the first one of the extra circuits that are the complex ones. And we're going to use this as an example to show you kind of what you're expected to do. So in this particular circuit, I've got one battery over here and I've got one, two, three, four, five resistors, although some of them are labeled A, B, C, and then the other one's four, five. And it has the particular resistances labeled next to the resistors as well. If I was wanting to find the equivalent resistance in this circuit, again, I want to identify subparts of the circuit that are either in series or in parallel. Now, one of the ways that you can do that is by first focusing on where is there actually a junction? And a junction is where multiple wires meet. Now, A is not a junction, even though it looks like I've got one wire in and one wire out, because it's really kind of a corner. But down here, I've got a junction, because one wire then splits into two. And down here, I've got a junction because the two wires come back together. Now, you see a split and come back together and you might start thinking about parallel, but let's look at what's happening on those branches to start with. So if I go from one junction point along these wires, I see that both of these are on the same branch. Now, this isn't a junction, again, it's a corner. So Rb and R4 are together on a single part of the circuit. And similarly, on this side, Rc and R5 are on a single branch of the circuit. So what that means is that these two sections are each series sections. Now, I could pull out my calculator here, but you should be able to see very quickly that if I combine 2 ohms and 18 ohms in series, well, in series, they just add.  So I really have a 20 ohm resistor on this branch. And again, you can do it in the calculator, but I'm saving these for later, even though you can probably do it in your head. 3 plus 12, not times, plus 12 is going to give me 15. And so over here on this side, I've got 15 ohms. So now I've got a 20 ohm resistor and a 15 ohm resistor if I think about it in terms of the equivalent resistance. Now, depending on how good you are at sort of seeing the shape of these things, you might want to redraw it. I've got a line that comes down here, then I've got another branch and a branch, and they come back together. And over here on this branch, I've got 20. Over here on this branch, I've got my 15. And up here, I still have my original 6. So this is like redrawing the circuit to show the simplified version. Well, now we can see a little bit more carefully that this part of the circuit is in parallel. Now, I don't do these ones so well in my head, so I'm going to have to come over here and do 1 divided by parentheses. Don't forget your parentheses here. 1 divided by 20 plus 1 divided by 15. Close my parentheses. And that's going to give me my equivalent resistance for this part of the circuit over here. Now, notice it doesn't really matter if I draw it vertical or if I switch it. So I'm going to go ahead and now switch it so that over here, I've got my 6 ohm resistor. And then I continue to what is now my new combination of the 20 and 15, which is going to be approximately 8.57. And fill that in as my 8.57. And what I see is that that whole thing now, the 6 and the 8.57, is an example of something, which is now in series. So how do I combine them in series? Well, I'm just going to add them together. So I'm going to have 6 plus 8.57. And that tells me that my equivalent for the entire circuit is a grand total of 14.57. So I've identified where my junction points are, saw that I've got some series sections, did those first, then see that those two series sections are in parallel. And when I replaced that, the remaining two were in series, giving me my final answer for the circuit of 14.57 ohms.


Purdue helped me by teaching me that you may not know the answer to this problem, but if you're willing to go out and work and find someone who does, you can achieve an incredible amount of things. I'm the active CEO and co-founder of Heeloponics and we provide consumers with the GrowPod, a rotary aeroponic appliance that allows them to have a greenhouse in their home and grow their own food. My co-founder Ivan Ball and I were simply building this as a hobby in our dorm rooms. This is a genuinely sought-after ability to be able to have control of your own food supply and that's when we realized that we had a real opportunity to scale a business from this idea. We use aeroponics which sprays the roots, they're able to get plenty of ambient oxygen from just the air in the room, so we've eliminated the likelihood of root rot, but we also have a self-cleaning apparatus that is significantly more energy efficient than anything before. Purdue made a giant leap in investing into our company when we won our first business plan competitions. That was a massive leap I think for them to take a risk with the startup and a massive leap for ourselves to hear that someone said, you have an idea and we want to see you follow through of that and that opportunity is rare and it's uniquely at Purdue. We've designed a farm that uses many of the utility patented concepts and our domestic high-tech version to make a cheap durable low-tech version for Africa funded by the Department of State through the Mandela Washington Fellowship and since we've created our farms and given lectures and actually given away the blueprints for these low-cost African farm designs, I have an incredible amount of people telling me thank you for showing me how to grow food. Vegetables that would have never been able to grow in that climate, food that people have never tasted in these areas, they now have and they've got a lot of sunlight, so there's no need for us to have grow lights there and we use hydroponics to add the soil quality characteristics that they simply don't have there. So we've left footprints truly around the world and I have to say it's a powerful experience when someone contacts you and says thank you for this food. Thanks to Purdue, I had the courage to pursue my business idea and turn it into a venture funded enterprise. That was Scott Massey, look for more stories at Purdue.edu.com.


Today is about us gentlemen. It's about each and every collective individual in this building today. It's about what you're willing to sacrifice for the man beside you. So today I want you to give me everything you got. Give me everything that's inside you. It's about getting what's everything ready to go in all towns, baby. For all more corners. It's a 60 minute ball game and it's time to go to work. Let's go!


Good morning. So, in the last lecture, we looked at how to incorporate effectiveness or rather the effective diffusivity or pore diffusion effects on the reaction kinetics. We again I will repeat like we have the reaction taking place in 6 steps. First is external mass transfer of the reactant, then internal diffusion, adsorption, reaction, desorption of the product, internal diffusion, back diffusion of the product and then the external mass transfer of the product. So, out of which we have already considered 3 steps adsorption reaction and desorption. Now, we are trying to incorporate the effect of internal diffusion. So, we have this catalyst particle and we are looking at the diffusion inside and this is external surface r is equal to capital R and this is center. I told in the last lecture that it is a porous particle. You have pores, actual moment of the particle will be torches, but all these effects the constriction, torchocity, porosity everything is incorporated in a term called effective diffusivity, DE effective diffusivity and when we write when we use this term effective diffusivity then we are free to write a normal fixed law for diffusion in the radial clock coordinates if the particle is spherical. So, in that case the flux becomes DE into DC by or DCA by DR of course, the minus sign. So, this becomes a flux. Now, what is the difference between this flux and the flux that is taking place in a non porous particle or other not non porous or as a continuous medium rather the continuous medium the D is an is a different diffusivity is a bulk diffusivity that we talk about normally. There is no effect of porosity, there is no effect of walls, no effect of the torchocity as well. So, this is a diffusion that is taking place in the radial coordinate, but then we are incorporating the effect of the solid matrix there in a porosity material effects. So, DE takes into consideration all those effects and then I can write as if it is a continuous medium inside a particle. We already discussed this at length in the last lecture. Now, what are the equations because if like why what we are trying to do here is to get the concentration profile inside a particle the concentration profile inside a particle. Now, we define dimensionless concentration psi is equal to CA divided by CAS where this is the external surface concentration it can be CAB as well. So, I can use these terms sometimes like either CAB that is bulk concentration or CAS that is external surface concentration because right now we are not considering external mass transfer effects. So, 5 so this is psi and then there is this lambda which is nothing but R by R is a radial distance R R is the sphere radius alright. Now, if we do this I get an equation for the concentration dimensionless concentration as d 2 psi by d lambda square plus 2 by lambda d psi by d lambda minus psi sorry not psi phi m square remember this psi raise to n is equal to 0. Now, what is this? This is a very important term this is very important term that tells you how important the pore diffusion effects are. Now, we call this as a Thiele modulus. Now, Thiele modulus is given by phi n square k n S A rho C R square CAS raise to n minus 1 divided by d e. So, we know the meaning of each and every term here k n is a rate constant per unit area right per unit area n denotes the order of the reaction and I am defining it for the order here n right S A surface area per unit weight of the catalyst rho C is the density of the catalyst mass per unit volume. So, this entire quantity k n S A rho C is rate constant per unit volume this is per unit area this is per unit these two together per unit weight and these three together per unit volume of the catalyst. And then we have these terms these are radius then your concentration order and effective diffusivity and this we can further simplify this or other further play with this particular expression and show that phi is the ratio of the intrinsic rate to the diffusion rate. So, it represents the relative magnitudes of intrinsic reaction rate and diffusion rate. And if value of phi is very large value of phi is very large in that case the diffusion resistance is significant. So, Thiele modulus if it is significant or substantial value or the very high value diffusion effects we cannot neglect them on the other side like if you have phi value very small say 0.001 in that case diffusivity effective diffusivity is likely to be very large compared to the intrinsic reaction rate or the rate of the reaction rate constant is very small. So, that it is diffusion is not important at all it is like open surface or the part or the molecules are getting access to every side without any problem concentration gradient inside a particle is negligible it is almost a flat profile. So, that is the meaning of phi all right. So, now we so, let us try and solve this equation now we go further we want to see the concentration profile and why we want concentration profile is to further calculate the overall reaction rate because you have not yet got the expression for the reaction rate to be used in the reactor design. So, we are heading towards it fine all right. So, this is the equation and this is the meaning of psi n boundary conditions we already looked at boundary conditions in terms of concentrations dimensional concentration now let us try and write them in terms of non dimensional concentration. So, psi is finite where at lambda equal to 0 very important right at the center psi is finite or d psi by d lambda is equal to 0 d psi by d lambda is equal to 0. Then next psi is equal to 1 at lambda is equal to 1 right why because at external surface at external surface lambda is equal to 1 r is equal to capital R and psi is equal to 1 because c a is equal to c a s right. So, lambda is equal to 1 lambda is c a by c s all right. So, we have these this differential equation with these boundary conditions now we need to solve this equation not so easy, but there are ways to work with it. So, if you assume the reaction to be say first order reaction solve it analytically first we have a variable called say y and which is defined as psi into lambda. Now if you do that and substitute for it in this equation then you can do some mathematical jugglery and get a equation in terms of y and lambda like this. So, d 2 y by d lambda square minus phi 1 psi by d lambda square minus phi 1 psi by d lambda square y is equal to 0. Now why 1 here because order is 1. So, this n here represents the order do not forget that. So, I am writing it for a first order reaction I am writing it for first order reaction I am making assumption that y is equal to psi into lambda the product of these two variables. So, what happens is I can get rid of psi here you can write d y by d lambda just differentiate with respect to lambda and then substitute here you can do that mathematical manipulation and what you get is this and this is a very simple equation to solve and there is a solution for this equation the general solution for this equation which can be given as y is equal to a 1 cos phi 1 lambda this is this is mathematics b 1 psi n h phi 1 lambda. So, this is a general solution for this equation with the boundary conditions of course, I have not applied those boundary conditions yet because now I have the equation in terms of two constants a 1 and b 1 which has to be found out with the help of boundary conditions and you know the meaning of phi 1 and lambda. So, what is y is psi into lambda. So, let substitute for y now and I get my equation that I want because y is a dummy variable there. So, substitute for y. So, what you get is psi is equal to a 1 divided by lambda cos phi 1 into lambda plus b 1 divided by lambda sin h phi 1 lambda all right. Now, we have to make use of the boundary conditions to get a value of a 1 and b 1. So, let us talk about the first boundary condition where at lambda is equal to 0 at lambda is equal to 0 lambda is equal to 0 you have lambda is psi finite. Now, look at this equation if this is lambda if lambda is equal to 0 then of course, this factor becomes 0 sin h you do not have to worry much about it, but then here this becomes 0. And this term is finite why? So, this term because cos 0 cos 0 tends to 1 right when lambda becomes 0. So, this is 1 this is 0 this is finite this term of course, taken care of because this is 0 this is 0 probably you do not have to worry much about it, but if this is 0 this is sorry yeah if this entire term is tending to 1 this is 0 and if you I am saying that this is finite then what should be the value of a 1? It is quite obvious if a 1 is finite a 1 is finite then this becomes infinite because this is 0 right, but this is finite. So, this is not true. So, a cannot be finite means a 1 is 0. So, that implies a 1 is 0 I will repeat this tends to this cos becomes 1 this becomes 0 this is finite this is anyway 0 by 0 tending to 0 by 0 that means this is this term is finite, but then if a 1 is not finite then this would become infinite that is not correct because psi is finite. So, that means that a 1 has to be 0 it cannot be any finite number I hope this is clear. So, once a 1 becomes 0 I can get a value of b 1 from the another boundary condition. So, let me first write psi is equal to b 1 by lambda psi in h phi 1 into lambda. So, let us apply the second boundary condition what is that second boundary condition? Second boundary condition is a 1 where you have at lambda is equal to 1 psi is equal to 1. So, this equation gives me the value of b 1 what is the value of b 1? So, 1 is equal to b 1 divided by lambda psi in h phi 1 right. Now, b 1 is nothing, but which implies b 1 is equal to lambda divided by psi in h phi 1. So, if you substitute for all the value of b 1 in this in this then I get a final expression in the form psi is equal to which is nothing, but c a divided by c a s we already defined it which is equal to 1 by lambda psi in h phi 1 psi divided by psi in h phi 1 psi in h phi 1. So, this is the concentration profile this is the concentration profile that we wanted of course, for the first order reaction for the first order reaction that is phi 1 first order reaction because it was easy for me to solve for this equation solve equation for first order reaction. How am I going to use this? See this is lambda sorry the way I have shown lambda here it looks like tau, but actually it is lambda all right. So, this is the equation for concentration profile I can substitute for lambda r small r divided by capital R and get the equation in dimensional form c a relation between c a and small r that gives me the concentration profile inside a particle. Now, before we go ahead and define certain parameters later we will look at a profile how it looks like. Now, we can always qualitatively draw a profile a concentration profile from this equation. In fact, we do not need equation initially to just imagine or the guess the profile inside a particle. How will it look like? You have r right r increasing in direction that means r is equal to 0 here r is equal to capital R here and then you have this concentration or you can write psi c a by c a s is better we do that because then I can I know what is the maximum value that is 1 all right. Now, this distance as I go from center to the external surface how will it look like where exactly it is going to be maximum it is going to be maximum at the external surface at the external surface it is going to be 1 here because it is c a is equal to c a s here right and inside. So, this is where I have bulk and particle started from here and it goes towards the center right. This concentration is going to go down. So, typical concentration profile is going to be like this and at r is equal to 0 at r is equal to 0 at center d c a by d r or d psi by d r is 0. So, it is going to be flat it is going to be flat look at this at this the condition is satisfied it is finite, but d c a by d r is going to be 0 symmetry all right. So, this is a typical profile that I am going to see this is a typical profile that I am going to see inside a particle. Now, this profile will depend on which parameter this profile will depend on just one parameter look at a differential equation there is one dimension less number that defines everything inside a catalyst which is nothing, but Thiele modulus phi ok phi n for nth order reaction phi 1 for first order reaction right and depending on the magnitude of phi this profile will change qualitatively it will look like this, but you can imagine now tell me if value of phi is very very small what does it mean value of phi is very small means that the concentration variation inside a particle is negligible ok. The profile is flat ok there are no gradients why because there is no pore diffusion effect the pore diffusion is. So, fast that a particle before the sorry not particle molecules before they react they immediately get into the inside a pores inside a particle and some of the concentration is leveled off ok it is exactly or which is quite close to what you have at external surface ok. So, for phi is very for very small values of phi this profile is flat ok. So, this is very small value of phi. So, let us say phi 1 or phi let me call general value of phi n ok which is very very small this is some intermediate value of phi and if the value of phi is very large then the gradients are significant ok. Then you can imagine something like this this is for phi n very very large very large value of phi n or phi 1 whatever depending on order of reaction importance of pore diffusion how it changes ok and how it is characterized it is only one parameter which tells you about importance of pore diffusion that is phi ok. I hope this is clear pore diffusion effects you should remember this no pore diffusion effects this is the one somewhere in between both are important reaction and pore diffusion I cannot neglect both of them. But suppose I am dealing with case like this then pore diffusion can be ignored whatever exercise we have done so far Thiele modulus of course, you have to calculate it first to know whether it is important or not not.  But then form for a catalysis person he should think why even if so it is like this he has prepared a good catalyst say platinum on alumina ok. And he has nice porous catalyst with very large surface area and it is nicely dispersed that means it is concentration is uniform everywhere inside a catalyst particle the concentration of p t is uniform what is p t platinum and I am using alumina as a support and platinum species are nicely distributed inside. Now imagine if value of phi is very very large a situation like this is it a good catalyst no why because the particle the platinum particles somewhere in the core somewhere in the core that is near the center are not seeing reactant molecules at all. Because you see the profile here is flat and almost zero concentration all the reactant molecules are somewhere near the external surface. So, what is the use of putting platinum there is useless unnecessarily I am taking efforts on preparing the catalyst dispersing it very well. But some of the platinum species or the sides are inaccessible why it happens because effective diffusivity is very small why the effective diffusivity is very small look at a expression of the effective diffusivity bulk diffusivity into porosity sorry Knudsen diffusivity into porosity into constriction factor divided by tortuosity. So, if the tortuosity is very very large effective diffusivity will go down if the porosity is very small pore diameter that matters the pore diameter is very small effects will be significant. So, the diffusivity so I need to design a catalyst now such that I will get rid of the pore diffusion effects. So, that this platinum is accessible or otherwise if I am happy with the platinum that I have put at a surface here and reactions taking place at a rate that I want then do not do this do not take efforts on dispersing the catalyst nicely just put a catalyst only in the exterior part or the part where it is very close to external surface only in this part. So, that is the meaning of it to this analysis helps the catalysis person the catalysis or the person who designs the catalyst very well. So, he needs to have the knowledge of pore diffusion effects. So, that is the meaning of all this. So, let us go ahead now. Now, we understood how the concentration changes inside a particle we are going to make use of this and get a rate equation that we want for the reactor design see the ultimate aim is to design a reactor ultimate aim is to design a reactor.  So, let us get back to our CSTR. So, suppose I have a CSTR in that I have this catalyst particles remember what did I write F A 0 minus F A plus R A into W is equal to 0 W is the weight of the catalyst and I express sometimes I put a dash here if you see notation in Fogler's book use R A dash here it is pouring it weight of the catalyst. Now, this equation I told you last time before we started our discussion on diffusion effects this term is nothing but the one that is obtained from either Langmuir initial mechanism or Euler ideal mechanism whatever taking into consideration adsorption, desorption and reaction. So, this particular term now what we are looking at is how this term is going to get modified if you have pore diffusion effects also present. So, that is the exercise we are doing say this is a design exercise I am just talking about CSTR can be applied to a plug flow reactor as well. But then what is the objective of this entire exercise that we have been doing is to look at this particular parameter the rate of reaction this variable how does it change now? How do we incorporate effect of pore diffusion effects? So, let us go ahead I have this equation concentration profile size is equal to C A divided by C A S is equal to 1 by lambda sin phi 1 lambda divided by sin H phi 1 for the first order reaction. Now, I am going to define a factor which is very very important and it is going to help us later a lot for the reactor design. So, what is that factor which is effectiveness factor? So, let me call this is effectiveness factor I am going to define this first and then get an expression for it this is effectiveness factor as a name says it tells me how effective is the catalyst how effective is the catalyst. Now, I have this particular factor is going to incorporate effect of pore diffusion if the effectiveness is very large that means, pore diffusion effects are insignificant. If the effectiveness is less then the pore diffusion effects are more. So, it works exactly opposite to Thiele modulus. Thiele modulus means if the effectiveness sorry if Thiele modulus is large then the pore diffusion effects are significant the resistance is significant. If Thiele modulus is small the resistance is small whereas, effectiveness factor is exactly opposite. So, we are going to see an inverse relationship between these two eta and phi that relationship is going to be inverse, but not so straight forward we will see how it works. There is an advantage you may ask me why you are defining two parameters or another parameter. So, it will be clear as and when we go and solve equations later because effectiveness factor tells you many things which are like quickly you can estimate the importance. Now, phi value can vary from 0 to infinity whereas, effectiveness factor will varies from 0 to 1 and sometimes it can be greater than 1 we will talk about it. Now, this effectiveness factor is nothing, but now listen to me carefully this is the observed rate this is the observed rate of the reaction or actual rate observed or actual rate. That means, if I do experiments whatever rate I get divided by now this is very important the rate calculated at external surface rate calculated at the external surface. Conditions how do you calculate the rate at external surface what do you need to calculate the rate at external surface you need external. So, you need concentration. So, this concentration is not a concentration inside, but the external surface concentration in our case it is C A S or C A B whatever you need temperature also we are not talking about non isothermal reactions so far, but then later on we will talk about that as well. So, I am just calculating rate at the external conditions it can be concentration can be temperature because for rate calculation I need temperature also because rate constant is function of temperature. So, I am calculating at external surface what does it mean let me write it down in words because this concept is quite important let me write down in words rate calculated at the external surface. It means that let us assume or let us consider a hypothetical situation where you have the surface which is present inside a catalyst the surface which is present inside a catalyst is opened up to the external environment to the external environment. So, this is your C A S what was happening before that the diffusion taking place some of the sides inside we are seeing less concentration than external surface concentration. Now, I am imagining a situation where entire surface is opened up. So, let it be say 500 meter square per gram let it be a football ground whatever a large external surface, but this is open to the external conditions. So, that C A S so, all the sides on the surface are going to see this. So, the rate calculated under those conditions for this concentration is going to be much larger compared to what it would be when calculated for inside particle when the concentration goes down in the presence of pore diffusion effects. So, the rate here is smaller because the concentration is less whereas, the rate here is large because all the sides are seeing higher concentration or larger concentration which is there at the external surface. So, imagine two scenarios. So, what I am doing is I am comparing this with this. So, rate calculated at the external surface is nothing, but rate when the area or all the catalytic species is exposed to the external condition. Conditions means C A S and T S I hope it is clear I am comparing these two scenarios comparing says in terms so, through eta. So, eta now eta is a rate for this divided by rate for this and this rate is going to be smaller. Most of the cases there are exceptional situations where this rate is higher will come back come to that, but otherwise in normal situation this rate is smaller than this rate. So, I am going to see the value of eta to be less than 1. So, value of eta is less than 1.  So, it depends like it can per unit volume it is per unit weight it can be R A dash divided by minus R A dash is it is all units that matter. So, dash is taking a per unit area then there is another thing called as per unit per unit surface per unit surface per unit volume per unit weight per unit surface sorry it would be other way round it would be per unit volume per unit weight and per unit area. So, whatever so, what we are doing here is we are looking at a rate which is observed rate actual rate divided by rate calculated at the external surface. So, we can say that say let us take this particular ratio that is minus R A dash which is per unit weight of the catalyst into mass of the catalyst divided by minus R A dash S into mass of the catalyst. What is the unit of this this is per unit weight of the catalyst into weight. So, it is the unit is going to be moles per second divided by moles per second. So, I am going to evaluate this or get the expression for this in terms of moles per second and substitute here and get a value of eta.  So, let me call this is m A divided by m A S divided by m A S that is moles per second reaction rate actual reaction rate divided by moles per second reaction rate calculated at the external surface. So, let us get the expression for m A let us get the expression for m A that is or rather m A S first that is easy to understand that is calculated at the external surface. So, it is rate per unit area into surface area per mass of the catalyst into mass of the catalyst right. So, rate per unit area is unit surface area is say k rate constant into C A S into surface area I am calculating at external surface. So, C A S into surface area S A right in terms of density mass of the catalyst is rho C into fourth third pi r q alright. So, this is m A S I am going to use this later.  Now, how do I calculate the observed rate? Now, I know the concentration profile inside the catalyst let us assume first order reaction now I know that psi is equal to whatever that psi in h 5 1 lambda divided by psi in h 5 1 right. So, that concentration profile I know now you have this catalyst particle inside which there is a concentration gradient right and then I know what is the gradient at external surface. So, if I am sitting at external surface I know how many molecules are going inside how many molecules are going inside at steady state there is no accumulation inside. So, if I am at the external surface and just watching number of molecules going inside a particle calculate the rate there calculate the flux there then that is nothing but the rate of the reaction. Because whatever happening inside the gradient that is generated will is based on the reaction that is taking place inside is because the reaction takes place inside that you have a gradient that you have the gradient inside is because of the reaction. So, I am taking into effect or taking into account effect of reaction. So, if I am sitting here and just observing number of molecules going inside then it is the rate of the reaction. So, how do I quantify it? How do I quantify it? It is nothing but a flux at the external surface into area into the area what is the area? Area is this external surface area and flux at the external surface. So, it is nothing but 4 pi r square d e into d c a s 4 pi r s by d r or in a dimensionless form or other if I just want to get a gradient in the in terms of psi that we have defined earlier it is going to be d psi by d lambda at lambda is equal to 1 not sorry here it should be c a and at the external surface that is r is equal to capital R. So, I have this particular expression for the actual rate. So, this is the actual rate number of molecules going inside per unit time. What is the unit of d e into d c a by d r? This is moles per second per meter square per unit area and I am multiplying it by area. So, the unit is moles per time let me write it. So, this has a unit moles per meter cube that is concentration into meter that is radius this is unit of d c a by d r what is unit of d e unit of d e is meter square per second. So, what is the unit of this product moles per this meter square into second and if I multiplied by area in which you have r square. So, meter square so, moles per second the unit of this entire thing is moles per second unit of m a that is what I want. So, look at expression for eta that we have got. So, this is eta eta is m a divided by m a s and this is nothing but moles per second divided by moles per second. So, I have got expression for m a and m a s. So, I am just going to substitute for m a and m a s in eta and see what I get. So, eta is equal to m a that is 4 pi r square c a s d divided by m a s k 1 c a s s a rho c 4 third pi r cube. So, this is eta. Now, I can get expression of for eta if I know this and this is something that I have already calculated or rather I know d psi by d lambda I substitute for lambda is equal to 1 and I get the expression for this. So, how do I get that psi is nothing but 1 by lambda sin h phi 1 lambda divided by sin h phi 1. This can give me d psi by d lambda and if I substitute for lambda is equal to 1 what I get is d psi by d lambda at lambda is equal to 1 is equal to phi 1 cot h phi 1 minus 1 phi 1 is Thiele modulus for the first order reaction. You can do it just a mathematical. So, you have you can get a value of d psi by d lambda at lambda equal to 1 substitute for this in the expression for the effectiveness factor. Substitute for this in the expression for the effectiveness factor here. What do you get? It is going to be a big explanation, but easy to understand just doing it systematically. So, you know the meaning of each and every term there. So, eta is equal to 4 pi r d e c a s phi 1 lambda sin h phi 1 lambda sin h phi 1 cot h phi 1 minus 1 divided by k 1 s a rho c 4 third pi r cube into that is it. So, this is the expression for eta.  And this what is this? This is nothing but the Thiele modulus. So, I have eta equal to 3 divided by phi 1 into square into phi 1 cot h phi 1 minus 1. So, I have got expression for eta in terms of phi. This is what I wanted. I told you there is a relationship between phi and eta and this is slightly complicated relationship. We will continue with this in the next lecture and I will tell you more about it. But remember as phi increases, eta decreases. Effectiveness factor is more means catalyst is effective, porosity or pore diffusion effects are less. So, we will continue with this in the next lecture. Thanks.


This is stock number 9662 we are here at Summit Automotive in Fond du Lac, Wisconsin You're new and used SUV headquarters today We are checking out this super clean 2008 Hummer H3. This vehicle has the 3.7 liter 5 cylinder motor from this HD video You will be able to tell that this Hummer is extremely clean all the way around inside and out Front bumpers in excellent shape. I didn't see any major dents or dings on it Factory fog lights headlight lenses are nice and clear nice bright white color We shoot all of our videos in 1080p So if you have HD capabilities on your computer tablet or a smartphone device turn them on now because it is like you're right here Looking at the vehicle with me as the factory alloy rims with the Bridgestone dual or 265 75R 16 tires And these tires are like new on here. I'd say 95% of the tread or more left Front fenders in excellent condition. I didn't see any dents or dings on that. The hood is in excellent shape And I apologize if I go a little fast and trying to get this done before my camera overheats here factory alloy rims, it's about 100 degrees with the heat index today and humid As we go down this side of the vehicle you can see just how clean that body is how reflective and Mirror like that paint is we take these HD videos So if you are far away or even if you're close by and just cannot make the trip down You can still see the vehicle hear the vehicle and have confidence in what you're looking at before you even get here Back tires have just as much tread as the front tires and those rims are in excellent shape Frame and underbody is in really nice condition on this ride It's like that all the way underneath lower rockers look really good it has Factory painted step bars that are in nice condition. I Didn't see any dents or dings on those doors As we come around to the back here. The rear bumper is in excellent shape. It has a matching Rim that's a nice shape as well Back storage area is very clean too. No rips or tears back here and those seats do fold down for extra storage Gate shuts nice and solidly Very clean on this side and As you go down this side of the vehicle just as clean as the rest of the vehicle For full disclosure this back room is in nice condition as well and that back tire has just as much tread as the rest Denser dings on these doors does have power mirrors Inside this one has the base package Seats are in really nice condition Power driver seat with lumbar factory floor mats Power windows power locks and power mirrors This one has auto headlamps and as we hop inside here You can see that this vehicle has fifty eight thousand three hundred and twenty three miles Instrument cluster is nice and clean steering wheel is in excellent shape has a push button four-wheel drive CD player and Your climate controls are right there. The dash is very clean on this vehicle You do get a compass temperature display in the mirror On-star capabilities as well factory floor mat passenger seat very very clean no rips or tears on that and The headliner is in really nice condition as well We'll take a quick look at the back seats and then we will check out under the hood Back seats are just as clean as the front seats no rips or tears back here Does have the latch child safety system and Factory floor mats back here this seat pops out and the back comes down Do you kind of need two hands to make that operate? Same thing with under the hood here Takes two hands to get it open Under the hood we have the three point seven liter Five-cylinder motor engine base very clean runs very smooth This vehicle has been fully safe to and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off and This H3 is 100% ready to go to see more pictures of this video or this vehicle in one of our other 400 new and used cars trucks SUVs Mini vans Wrangler's you name and we got to go to our website www.SummitAuto.com full pictures and descriptions of every single vehicle on our lot videos of every single used vehicle that we have All at www.SummitAuto.com if you want to make this one yours give us a call right now<PHONE_NUMBER> ask for one of our sales associates to make this Hummer H3 years today once again That number is<PHONE_NUMBER> and if you want to check out more videos you can go to youtube.com Summit Auto remember to like subscribe and share on this video and all the videos that you see there in fact in a second You'll see links to subscribe to our YouTube channel on your left a link to more inventory videos like this one on your right If you've not been to our website on the bottom link to this vehicle on our website click those check us out We really look forward to helping with this super clean 2008 Hummer H3. Thanks again


Hey you guys, so I am back today for a long-awaited review of the Camille Rose leaving conditioners About two weeks ago. I purchased the honey hydrate leave-in and also the herbal tea Sil and soft softened now I purchased both of these through her website Camille Rose She did have a cell gone on a couple of weeks ago one of my subscribers told me about it I didn't purchase it at the time because I wasn't sure Literally a week later. I went ahead and purchased it because shipping through her is very cheap It's like six dollars flat. You cannot beat that. Let me start taking my hair down y'all You can't beat that get to the punk girl. She no longer has these on her website to sell individually They are listed as the collection all three products. I was able to get these at $14 each Including the six dollars shipping. So let's get right into the review heads up I'm going to be moisturizing my hair in real time because I want to talk to y'all about something. Yes, so anyway Hair is looking very very full and fluffy because we are at two weeks semi-mini twist I took them down kind of separated My hair is a little raggedy on the ends. I wouldn't say it definitely needs to be moisturized, but Um Yeah, she she needs a little bit of moisture So those of you who are familiar with the LCO method that is liquid cream oil I'm using the Jane Carter solution quench curl hydrater as my liquid and of course the honey Hydrate leave in by Camille Rose as my cream cream quote-unquote and the herbal tea silt and soften as my oil So let's just get right into the consistencies that smell and all that good jazz First of all, this looks like real honey, I can't leave it in here because my husband would definitely put it in his tea. Oh That smells good. That smells. You know what?  No, it smells like a whiskey It really does to me it's well, you know how some whiskies have a honey Type scent. I mean some whiskies are to have that sweet type of smokiness smell. It doesn't smell. I shouldn't say that it smells good Let's get into a little bit of the consistency. Oh, so you know what? Hold on y'all Let me shake this up first. Okay Does that oil in it it has castor oil, okay, let me shake it up All right, now let's get into the consistency. It's like honey This consistency is just like honey and it has quite a bit of castor oil You can see how shiny my finger is so with that And since it's a liquid leave in it is I wouldn't say it's it's not like your traditional leave-ins I'm Guessing that I won't need to use a lot of this I would literally use like drop to this now I'm also considering doing a hot oil treatment if you guys are interested in seeing that just with this product alone Because there's a lot of it I will do a hot oil treatment if you guys are interested even hell I could try this as a pre pool mixing it with a conditioner and see how this works because Um, yeah, so I sex it off my hair I don't want it. You know really damp. I'm gonna take the leave in About 15 cents worth Yeah, y'all, I don't think I'm gonna use Hardly any of that oil if I do I will use it towards my end. This feels so good And it really does feel like honey The consistency is just like honey. She was able to get that from the castor oil is what I'm guessing Okay, and I'm gonna take just a little bit of The herbal tea and let me smell it It smells like tea Mmm Nettle leaf and sage. I just want to say I smell sage. Nettle leaf and sage Um Some of the ingredients so that's it. That's all I'm using This is a very lightweight oil. So look y'all this is what I want to talk about Or any of y'all canceling echo salad gel Look I've been saying I've been watching the the you know videos and look you guys I am a huge lurker I do comment on videos um And I know some of y'all see me and I see some of y'all But these last few echo salad gel is canceled They trying to kill black women That's not funny But what is Comical to me is the fact that and I'm just gonna twist my hair up once I'm done with each section and probably should make They look a smaller girl so There was one very popular actually a couple of popular youtubers who have been making videos about this Echo salad gel This is how I feel you guys This is my honest opinion y'all see me use echo salad gel Mostly it's for wash and go. That's what a lot of you know a lot of naturals use it for I don't really do wash and go. Y'all know how I feel about it. Um I really don't use echo salad gel So let me tell you something if your product is going to cost two dollars to some change Because that's how much it is unless you get the really big one Which sells for four dollars to some change if it is costing less than five dollars What makes you think that there are going to be organic all-natural ingredients in this product? Hell I've gotten it on clearance for 99 cents. I'm not expecting Gucci Results on k-mart prices. That doesn't make any sense to me. So if you're looking for all natural ingredients great products You need to be purchasing products from those type of lines Echo salad isn't it baby? It is not if you can find it at one more for a couple of dollars Do not be quick to jump on the bandwagon before you do your own research Okay, like I said, I have a jar of echo salad gel in here. I don't use it as much um Because it's just not a good it's not a good product. We have to know how to pick our battles you guys I mean Unless you are using the echo salad gel every day Which god bless you if you are a girl unless you are using the echo salad gel every day What they're really poising us in is our food that we are ingesting in eating every day Now we'll also say this I don't know if it was the echo salad gel or ic pentasia gel One of those gels when I was using it my eye started watering up and that is a side effect That's that's a chemical that's causing that reaction. So yeah Coming back on camera in about two to three more hours To show you guys what my hair looks like after I've allowed the products to kind of dry some Okay, so it's been a couple of hours and so i'm going to take down this section right here in the front um When I squeeze my hair I do feel a little oily However keeping point that I think most of the time when we use a leave in it's like a day or two Um, it's been a couple of hours. So let me go ahead and take down one. Like I said Yeah, my hair feels extremely soft. I will say that this is what it looks like up.  It's been two weeks and it smells good because of the honey leave in Very very nice. Let me take down one more. My hair is very soft. I know I keep saying that Look at that the shine So What I used to products again, absolutely with this in mind I would use the leave in on wet to um freshly washed hair preferably Because I feel like it's a type of leave in that if you're not careful if you use too much Um that it could cause a little bit of buildup not really I don't feel that way right now, but it's a potential that it could Um, but yeah when I use it the next time it will most definitely be on freshly washed Damn hair like the oil very lightweight. I definitely will be doing a hot oil treatment with that and possibly a pre-poo I'm going to go ahead and twist this Last one back up And that is it you guys. Um Thank you so much for your patience over the course of the last two weeks. I've been out And yeah new content is definitely coming. Thank you so much for watching. Take care. Bye


Hi everyone, welcome again to the spontaneous ACIM workbook lesson of the day and today we're doing lesson number 23 on the 23rd day of January here. I can escape from the world I see by giving up attack thoughts.  In fact, for those of you that are doing the lessons, you know, you may sometimes wonder as you're going through the lessons, why? Why is this true? Well, this lesson today explains everything. So it's the reason that the first 22 lessons are true. This one really explains it. So we'll go into it together here. I can escape from the world I see by giving up attack thoughts. The idea for today contains the only way out of fear that will ever succeed. Nothing else will work. Everything else is meaningless. But this way cannot fail. Every thought you have makes up some segment of the world you see. It is with your thoughts then that we must work if your perception of the world is to be changed. If the cause of the world you see is attack thoughts, you must learn that it is these thoughts which you do not want. There is no point in lamenting the world. There is no point in trying to change the world. It is incapable of change because it is merely an effect. But there is indeed a point in changing your thoughts about the world. Here you are changing the cause. The effect will change automatically. The world you see is a vengeful world and everything in it is a symbol of vengeance. Each of your perceptions of quote external reality is a pictorial representation of your own attack thoughts. One can well ask if this can be called seeing. It is not fantasy a better word for such a process and hallucination a more appropriate term for the result. You see the world that you have made but you do not see yourself as the image maker. You cannot be saved from the world but you can escape from its cause. This is what salvation means for where is the world you see when its cause is gone. Vision already holds a replacement for everything you think you see now. Loveliness can light your images and so transform them that you will love them even though they were made of hate for you will not be making them alone. The idea for today introduces the thought that you are not trapped in the world you see because its cause can be changed. This cause this change requires first that the cause be identified and then let go so that it can be replaced. The first two steps in this process require your cooperation the final one does not. Your images have already been replaced by taking the first two steps you will see that this is so. Besides using it throughout the day as the need arises five practice periods are required in applying today's idea. As you look about you repeat the idea slowly to yourself first and then close your eyes and devote about a minute to searching your mind for as many attack thoughts as occur to you. As each one crosses your mind say I can escape from the world I see by giving up attack thoughts about whatever the thoughts are hold each attack thought in mind as you say this and then dismiss that thought and go on to the next. In the practice periods be sure to include both your thoughts of attacking and of being attacked. Their effects are exactly the same because they are exactly the same. You do not recognize this is yet and you are asked at this time only to treat them as the same in today's practice periods. We are still at the stage of identifying the cause of the world you see when you finally learn that thoughts of attack and of being attacked are not different. You will be ready to let the cause go so there's some key ideas in there first of all again we're being reminded that the mind is causative and that the world is a projection of ego thoughts of attack thoughts so the world of images the body all the bodies all the circumstances all the situations everything about time and space that is an effect you might say if there was a big bang the big bang was the belief in separation in the mind and the cosmic time space cosmos is the effect and everything is part of those unreal effects from an unreal cause the egos and unreal cause and all the things even the electrons the molecules the atoms all the way up to the the cells the the body the bodies and on and on off to the cosmic gases black holes and stars and planets and spheres solar systems galaxies all of it they're all a fact of the belief in separation from god they're all a fact of the belief in in a fall from grace and the good news jesus is telling us is that the images have already been replaced and he's working his way to saying there's like three steps and the first two you know you have to require your cooperation so you have to really identify the cause of the world as as these attack thoughts in the mind and then you have to not protect them you have to literally give them away and when you give them away basically that's that your images have already been replaced so you first have to identify the cause and then let go when we say let go and let god we're really meaning let go of attack thoughts in the mind let go of judgments in the mind let go of grievances in the mind let go in the end of of all of your thoughts of the past and all of your thoughts in the future and when we say let go we're talking about positive thoughts about this world and negative thoughts about this world the positive thoughts are are shadows of the light and as i've said earlier the the negative thoughts are are darker shades are dark shadows and basically you can't experience the light directly and the freedom of abstract love and and unconditional love and spirit as long as you hold on to the positive thoughts or the negative thoughts so all those old ideas about accentuate the positive and eliminate the negative we'll say uh don't hold on to either the positive thoughts or the negative thoughts because they're both judgments they're just judging in different directions and the final point of this lesson is basically saying that we're just identifying the attack thoughts as the cause of the world but but you'll notice that there will be a temptation to make a distinction between thoughts of attacking and being attacked and Jesus is telling us they are the same and everyone knows that thoughts of a victim victimizer attacker attacky you know the one who's doing it to someone and the one who's being done against all of those are part of the system of duality that the ego invented to keep the mind guilty so in the end all attack thoughts meaning thoughts where you perceive that you're being attacked and thoughts where you perceive yourself as attacking you have to begin to open up your mind to start to see that they're the same and when you do when you finally learn that thoughts of attack and being attacked are not different you will be ready to let the cause go okay practical uh considerations um I have a question that was written me just today on a couple different platforms it's from uh Jamuna in Hawaii aloha brother what do you do when forgiveness seems to be going nowhere that nothing is happening so you've prayed for help and and you feel like your forgiveness practice forgiveness seems to be going nowhere but when I first read your question Jamuna I thought of that line in A Course in Miracles where Jesus is saying forgiveness is quiet and silently does nothing it looks and waits and watches and judges not so forgiveness is the state of mind as it relates to our lesson today that is pristine that is free of attack thoughts it's like a state of mind that is not reached through any doing or not doing in the world because the world is in effect so when we say it's going nowhere when you've mentioned forgiveness seems to be going nowhere I think it's because that forgiveness is associated with form and oftentimes people say well I've tried to forgive I've tried to forgive all the people that I've ever had a grievance with or anyone who comes to mind that I feel upset with I've tried to forgive it the bible says forgive 70 times seven I've tried that it doesn't seem to be that that that is the number and and basically it's because there's still the belief in an external world and external causation and as long as there is the belief in externals from the mind that that's what projection is and then projection seems to be a trap for the mind in which you pray for help and then you wonder wow why why am I not able to forgive and for many centuries after Jesus taught forgiveness 2000 years ago many many centuries people have been trying to forgive but this is where the metaphysics come in where you start to realize that that you're not trying to forgive something that is outside of your mind you're actually trying to forgive attack thoughts that you still believe are real and those that belief in the reality of attack is something that really needs to be questioned exposed released so you could say that even the lesson implies just allow yourself to be aware of any attack thoughts and he says search your mind for these attack thoughts but these unconscious attack thoughts will seem to keep arising and arising and arising until the impossibility of attack is realized to have an attack you have to have two you have to have an attacker and an attack II to have mistreatment you have to have to you have to have one who's mistreating and one who's being mistreated that's duality that's the duality of the ego in the world the world is a projection of the ego belief system it's a projection of attack thoughts and in this projection there seems to be opposites hot and cold fast and slow high and low beautiful ugly you know on and on and on it just goes cold and warm it just keeps going and going male and female and on and on and on and basically what we see is these are the attack thoughts of the ego it's not just what people call condemnation but it's actually just trying to believe in images and give images a reality I know sometimes people say well what what does what does this situation mean in and of itself or what does what does this phone call that I just got mean in and of itself nothing means anything in and of itself because nothing is in itself the mind is whole the mind is complete everything is under the laws of God the laws of love so this distorted perception is what we're looking at today and we're basically using the lesson I can escape from the world I see by giving up attack thoughts this is like an expanded version of what Jesus taught 2000 years ago when he said judge not lest ye be judged this this is a modern day version of that here we are 2023 and this is what we're dealing with right now okay and we also had a question that came in recently from Sarah Antony in the United Kingdom and it's making a little bit of a reference to to a workbook lesson I I did recently which was lesson number 17 Sarah writes thank you for these live sessions David so helpful on top of your pre-recorded text lessons playlist so here is my question regarding lesson 22 and it follows on from the question covered in lesson 17 session let's take the same situation that our friend who is a mother of a troublesome teen teenage son who cannot be persuaded to stop being on his phone computer games I understood the principle within your answer to change our mind rather than to change the world the analogy that it isn't the TV channel but was the TV that is faulty was very helpful so I'm starting to get the point that this is all about retraining healing our minds but maybe I don't really truly get it because I still want to know what to do in the interim as it seems after nearly four years with the course it is a gradual process so what does the mother do should she be completely passive about a son so nothing but focus entirely on practicing the lessons or is there a course guided aka spirit guided action what is the right action in this situation many much gratitude for these sessions hoping I get lucky and my question is picked I will be listening well the thing that we need to remember first of all is a lot of spiritualities talk about right action and what Jesus is teaching us in the course is what you do comes from what you think so that's why he said in the lesson I just read today workbook lesson 23 it is it is with your thoughts that we must work because the change can only take place in shifting from a mind that is thinking attack thoughts to a mind that is not thinking attack thoughts a mind that either is ego invested or a mind that is fully invested in the Holy Spirit what Jesus calls these two aspects of mind is the right mind and the wrong mind the right mind is where we get the guidance from Jesus and the Holy Spirit and the wrong mind is the misperception of an external problem that's not out there because there is no out there out there so so basically you're asking for the practicality and the practicality that I always talk about is is guidance when you really are able to be open and tune in and it takes a lot of focus and practice you receive guidance and I've counseled many people and many mothers who have shared the same kind of question and we will have a joining there and join in deep prayer and sometimes there is a guidance for setting some guidelines in the world you know they talk about setting boundaries and limits Jesus would say follow your inner guidance and there may be times when a guidance comes through that is a it's always a temporary measure but it's also designed to bring your mind toward the light toward the present moment so even when there's guidelines that are set in a situation with maybe with a child who's spending all their time much of their time on a computer or a phone playing games which was what came up the question that she's referring to here so basically the guidance is so so important but the guidance is always to bring you to the present moment it's always to unwind you from the self-concept the guidance is always to collapse time to save time to bring the alpha and the omega together as Jesus taught I am the alpha I'm the omega you know in other words I am the beginning and the end I am the presence of love that's guiding you right now to remember your true identity through forgiving and releasing all attack thoughts all judgments all grievances so these kind of guidance has may come and even when the guidance has come and you're you're guided to deliver the guidance still you are not in charge of the outcomes of the world you're not in charge of the behavior of the body what you do comes from what you think and we're not to draw conclusions and draw interpretations based on the bodies we're asked to follow the Holy Spirit's interpretation to see the forgiven world every single situation you could just take one lesson from the course I could see peace instead of this and it's an invitation inward to the mind and to the stillness and you can see that that as long as there's investments and outcomes whether it's with anybody's behavior a child's behavior in this case or anybody's behavior it's always coming back to to the to the belief that there's something causative in form and something needs to be corrected in form and Jesus just told us in the lesson today lesson 23 you know there is no need no use lamenting the world he said there is no use trying to change the world so we're coming back to that beautiful presence in mind seek not to change the world seek rather to change your mind about the world he says it in different ways but it's it's the same teaching it's the same thing to practice all the time so with these two questions also what was coming to mind is when people read the lesson for the day I can escape the world I see by giving up attack thoughts sometimes they'll have a thought like wow easier said than done or I don't know if I can do that you know the ego will doubt that you have the power to change your mind about your mind to to fully give up the belief in judgment the fully give up the belief in attack thoughts all of them every single attack that emptied completely gone released and the doubt will come in sometimes and sometimes the doubt is associated with things that are preferred in this world things that the mind is attracted to there's three subsections in the text back to back the attraction to guilt is one subsection the attraction to pain is another subsection followed by the attraction to death and and really you can start to see that if the images are just illusory images and they're just effects of the ego's thought system and the ego's belief system then you can't really arrange these false effects into hierarchies of of positive effects and negative effects positive outcomes negative outcomes you can't judge the world when when Jesus is saying judge not he's saying escape this world by escaping its cause meaning escape the world which is the ego's world by escaping the cause of the world which is the ego escape the ego let go that ego he's telling us let let it go let go of all attack thoughts let go of grievances the grievances hide your light they hide that you are the light of the world they hide your Christ light if you hold on to grievances so I thought as an incentive I would just give a little glimpse of okay what happens if I empty my mind and I let go of attack thoughts what if I really thoroughly go all the way with lesson 23 here and I I totally start to realize I can escape from the world I see by giving up attack thoughts and so I was praying this morning and I was given a little a subsection from chapter 17 and chapter 17 is titled forgiveness and the holy relationship and I was guided to section two which is called the forgiven world this is our incentives this is whenever you have those doubt thoughts so you think what am I going to have to give up that I still value what am I going to have to give up that I still want whenever you look to the world or to the body and you think oh there's still some some goals and outcomes and things that I want from the world what's the incentive to say I can escape the world by giving up attack thoughts well the incentive is the forgiven world the real world the happy dream a dream of non-judge and non-judgment that that is the incentive so I'm going to read a little bit of this you know so you can get a feel for how wonderful the real world is because once you start to feel your heart connecting to the real world then the judgmental world of the ego is not going to hold any sway any attraction talk about fade and fade and disappear and disappear of course that happens to the projected ego world because you don't value it anymore but let's look at closely what is valuable which is the step between the distorted world and the kingdom of heaven it's the forgiven world it's it's the forgiven world of of non-judgment this is called the forgiven world can you imagine how beautiful those you forgive will look to you in no fantasy have you ever seen anything so lovely nothing you see here sleeping or waking comes near to such loveliness and nothing will you value like unto this nor hold so dear nothing that you remember that made your heart sing with joy has ever brought you even a little part of the happiness this sight will bring you for you will see the son of god you will behold the beauty the holy spirit loves to look upon and which he thanks the father for he was created to see this for you until you learn to see it for yourself and all his teaching leads to seeing it and giving thanks with him this loveliness is not a fantasy it is the real world right and clean and new with everything sparkling under the open sun nothing is hidden here for everything has been forgiven and there are no fantasies to hide the truth the bridge between that world and this is so little and so easy to cross that you could not believe it is the meaning place of worlds so different yet this little bridge is the strongest thing that touches on this world at all this little step so small it has escaped your notice is a stride through time into eternity beyond all ugliness into beauty that will enchant you and will never cease to cause you wonderment at its perfection we're getting words in there enchant enchanted wonderment perfection this step the smallest ever taken is still the greatest accomplishment of all in god's plan of atonement all else is learned but this is given complete and holy perfect no one but him who plans salvation could complete it thus the real world and its loveliness you learn to reach fantasies are all undone and no one and nothing remains still bound by them and by your own forgiveness you are free to see yet what you see is only what you made with the blessing of your forgiveness on it and with this final blessing of god's sign upon himself the real perception born of the new perspective he has learned has served its purpose the stars will disappear in light and the sun that opened up the world to beauty will vanish perception will be meaningless when it has been perfected for everything that has been used for learning will have no function you know it this section is just who just flowering of enchantment and wonderment and joy and love and and this reminds me of a couple workbook lessons we'll get to in this year 128 the world I see it was nothing that I want and then 129 beyond this world is a world I want he'll just keep coming back with this he's going to keep enchanting us back to the kingdom of heaven reaching us through the wonderment of the miracle the wonderment of a child that beholds innocence we're going to keep opening and opening and opening our hearts and minds to this beautiful real world and it's it's not so much learned as it is given this is a gift from the Holy Spirit some of you who are aware of the bible you know there's you're aware of a very famous passage in the bible and john for god so loved the world that he gave his only begotten son that whosoever should believe in him should not perish but shall have eternal life and jesus says well there's just one minor correction to that passage for god so loved the world that he gave it to his only begotten son and what he means by that is when the sun seemed to fall asleep and dream of separation from god dream of war and pestilence and disease and and greed and on and on then the real world was given as as the correction the real world is the Holy Spirit's gift to the sleeping son of god and if you feel like something is holding you back from forgiveness it's just that you haven't reached a point of of saying i want to see the real world i want to accept the gift of the Holy Spirit i want to accept the correction of this error called ego if from a christian term if if you were aware that there seemed to be this fall from grace and this uh this uh entity called satan well what if that entity of satan is a belief and that is a false belief let's just say that god is really love and that satan is the belief that you can separate from god and have an identity apart from god that's the definition of satan and if if you give it back if you give up all the attack thoughts of ego all the attack thoughts of satan and you really do sincerely take the lesson today i can escape from the world i see by giving up attack thoughts what you're really doing is then you're saying and i'm open to receive what has been given to me as a gift for the sleeping mind to wake up and remember the truth to remember christ to remember heaven and and to receive that gift is requires to release the attack thoughts you can't hold on to judgments and grievances and attack thoughts and still receive the gift because you're not ready uh basically jesus has told us in the lesson today you know if you still are not willing to release the attack thoughts then you're not ready to release the attack thoughts and underneath that is is still wanting to hold on to something that god didn't create so if god creates only love and god gives only love which is the truth perfection love eternity extends perfection love eternity innocence extends innocence you know it's just the way of creation uh everything that comes from god is like god uh perfectly like god and then when you try to deny that you're literally pushing holding off the holy spirit's gift of the real world so wow what a beautiful lesson today and i'm glad that we got uh the question from jamuna about you know what if it's not working and and also the last lesson that we learned the last question was from sarah anthony and basically that was answered in the sense that that you do follow guidance that that uh when we talk about passivity we could say that the ultimate helpfulness of passivity is in the mind and that's what jesus said in the gospel of thomas be passers by uh meaning you can just watch the world and observe the world without judgment and then your mind is healed but it's not talking about passivity in terms of form otherwise what would be the point of the guidance you could be guided by the spirit into various actions and through following the guidance you can be taken back to that point of witnessing to the point of of of like seeing the world in a different way completely being a passers by to the world that's that's where it's all heading but i can say from the last 35 years for me there's been lots of guidance that i've received and that came through me either spoken through me or acted through me and this guidance has been very practical and very helpful if anyone thinks that jesus is not practical then then it's just a matter of tuning into the guidance and being intuitive and once you're a hundred percent intuitive you're much more ready to be a passers by be passers by to this world you're much more ready to watch the world with the holy spirit and accept the holy spirit's interpretation so thank you for joining in today and again write in your questions if you have questions come up or with issues and things that you would like me to address and let's keep it spontaneous but i i feel some some more lessons coming this week precious ones this week so let's let's meet again see you soon love you


Hello and welcome to another exciting episode of Josh vs. Will. I'm Michael and this is Ben. Hello. Today we will be providing blissful commentary as Will once again tries to fool Josh with another VapCap challenge. Welcome back Will, what are we going to be doing today? Today we are looking at the differences in the tips. Just the tips? Just the tips, correct. So we have a couple different devices here. We have the M2020, we have the new Vong, our new 2021 Omni, and our 2021 M. So what we are going to be doing here today is switching around the tips on one device and having Josh guess which tip is being utilized. I'm going to be blindfolded again, aren't I? So we couldn't find the blindfold. We did find however an old shirt. Michael, it looks like Josh will be blindfolded with an old Dyna Jam shirt. That's down pat. And it looks like Josh is thoroughly blindfolded. Time for Will to test it with the balls. We could not find balls, but what I did find was a very clean. It doesn't smell clean. Looks like Will is also using a sponge to test Josh's blindfold.  There's no reaction there. Woo! Swing and a miss. Will thinks fast. And it stays to the face. This smells funky. All right, enough shenanigans. Let's get this competition started. Looks like for the first tip, Will has chosen the 2020 M tip. Will is removing the 2020 M tip and placing it on the 2021 M stem in an attempt to fool Josh, but will it work? There's the click and the handoff. The 2020 M stainless steel tip has a longer heat up time than the 2021 M tip. And that may tip Josh off. I can already tell this is going to be very difficult. They're always difficult. And it looks like for the second tip, Will is choosing the 2021 M tip. Will is taking a risk going back to back with the two stainless steel tips. Josh is ready for the handoff. There's the click. And the careful handoff by Will. The airflow is a little bit more restricted for me, even while feathering the airport. So that kind of gives me some idea. I wonder if I'm correct in my hypotheses. Interesting observation from Josh. Will doesn't seem to think so. You know, Josh, you've never really gotten any better at this through the multiple videos that we've done. I don't think any of your projections have been really even close to being correct. I have more faith this time around, I think. No. And next up, Will is heating the new omni tip on the 2021 stem. There's the click. Josh just enjoys to question me, question my skills. And a cocky little quip from Will. That one seemed to hold the temp a little bit longer. So I'm guessing it's one of the heavier ones. I think Josh likes that tip. A tip of the hat from Josh to that tip indeed, Mabin. You mean tip of the shirt. Don't get cocky now. The last tip is the Vong. Josh with the lobster claw. Will with the blissful commentary. Get your own show, Will. Could we go through the first two again?  I think it may be time for a cliffhanger, Ben. Is Will a malfunctioning terminator for the future? Was Josh and this bunny separated at birth? I have more faith this time around, I think. No. Can Josh guess all four tips and finally beat Will? All these questions and more on the next episode of Josh versus Will, the tip. Thanks for watching this episode of Josh versus Will with blissful commentary. Don't forget to subscribe and ring the bells over here or somewhere. Very good, Michael.


to take charlie charlie we're gonna just on elbows again from the left hand side instead roughly 50 meters just to our left hand side that looks like probable sort of would you be able to see because obviously like bushes and that they would be able to see in advance from that side would that be a problem a flank yeah yeah


So what do we know so far? Well, on the 2nd of June 2023, at roughly 7pm, three trains near Bahanaga Bazaar railway station Odisha collided. Killing as we know so far 275 people and injuring over a thousand more. The Coromando Express was travelling along the Holra Chennai main line towards Chennai. It was signalled along the main line, but for reasons still unknown was routed onto a loop line into the back of a waiting freight train. The Coromando Express derailed and some of the carriages went into the path of the Ben Gao Uru Hara Express on the downline. Initial reports into the accident hint at an interlocking problem caused by glitch in the electrical system. It's still early days, but what we do know is this is a truly horrible tragic accident and a needless loss of life.