JEE main and advanced: The Second Law of Thermodynamics

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The inability of the first law to identify if a process can be carried out is remedied by introducing another general principle, the second law of thermodynamics. The first law does not restrict the direction of a process, but satisfying it does not ensure that the process will actually occur. When processes can not be given, this can be detected with the help of a property called entropy. A process does not happen unless it satisfies the first and second law of Thermodynamics.

The use of the second law of thermodynamics is not limited to identifying the direction of the processes. The second law also states that energy has quality, as well as quantity. The first law has to do with the quantity and transformation of energy from one form to another regardless of its quality. Preserving the quality of the energy is a main interest of the engineers, and the second law provides the necessary means to determine the quality, as well as the level of degradation of the energy during a process. Nature states that the total energy associated with a thermal source can never be fully and completely transformed into useful work. Hence, all work can be turned into heat but not all heat can become work.

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Classical Definitions

Definition of Kelvin-Planck

“It is impossible to build a properly functioning appliance, a single effect that absorbs heat from a temperature source and converts it into an equivalent amount of work.”

Definition of Clausius

“It is impossible to build an apparatus that operates in a cycle whose only effect is to transfer heat from a source of low temperature to one of higher temperature.”

Thermal machine

It is a device that operates continuously or cyclically and executes a certain amount of work as a result of heat transfer from a high temperature source to a low temperature source.

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The thermal machine allows to obtain a system that operates in a cycle with a positive work and a positive heat transmission.

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The figure corresponds to a scheme of the steam power plant which fits into the definition of thermal machine. The scheme is quite simplified and the study of real steam power plants is studied at the point corresponding to the Rankine cycle. The different quantities shown in the Figure are:

QH: amount of heat supplied to the steam in the boiler from a high temperature source (boiler burner)
QL: amount of heat released from the steam in the condenser in a low temperature sump (cooling water)
WT: amount of work delivered by the steam when it expands in the turbine.
WB: amount of work required to compress the water to the boiler pressure.

Thermal efficiency

It is the measure of the performance of a thermal machine and is defined as the ratio between the net work obtained and the heat supplied to the working fluid

Thermal efficiency = net work / given heat

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since the sum of the heats is equal to the sum of the works for a system that performs a cycle, the net work can be expressed as:

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Refrigerator Machine

It is a device that operates continuously or cyclically, requires work and carries out the objective of transferring heat from a body of low temperature to another of higher temperature. The working fluid used in the refrigeration cycle is called refrigerant. The most commonly used refrigeration cycle is the steam compression refrigeration cycle, which includes four main components: a compressor, a condenser, an expansion valve and an evaporator, as shown in Figure. The refrigerating machine can work as a refrigerator or as a heat pump. Refrigerators and heat pumps operate in the same cycle, although they differ in objectives. The objective of the refrigerator is to keep the space cooled at low temperature by removing heat. The discharge of this heat to a medium of higher temperature is only a part of the operation, not the purpose. The goal of a heat pump is to maintain a warm space at high temperature. This is achieved by absorbing heat from a low temperature source, such as cold outside air, and supplying it to a high temperature environment such as a home.

Operating coefficient

The efficiency of a refrigerating machine is measured with the operating coefficient that comes to be the equivalent of thermal efficiency in a thermal machine. For a refrigerator, the operating coefficient b is expressed by

For a heat pump, the operating coefficient b is expressed by

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It is important to note that in a refrigerator the heat of interest is QL since this is the one that is extracted to cool a space. In a heat pump, the heat of interest is the QH since it is the one that is rejected to heat a space.

The Carnot cycle

It is a reversible cycle formed by four reversible processes which allow to obtain a greater efficiency of the cycle since the net work can be maximized by using processes that require the least amount of work and deliver the greatest amount of it.

Reversible cycles can not be achieved in practice because the irreversibilities associated with each process can not be eliminated. However, reversible cycles provide higher limits on the performance of real cycles. The thermal machines and the refrigerators that work in reversible cycles are models with which the thermal machines and the real refrigerators can be compared. Reversible cycles also serve as starting points in the development of real cycles and are modified as needed to meet certain requirements.

The Carnot cycle was proposed in 1824 by the French engineer Sadi Carnot. The cycle consists of four reversible processes, two isothermal and two adiabatic, and can be run either in a closed system or in a stable flow, with pure substance or with a gas, Figure 2.23. The four reversible processes that make up the Carnot cycle are the following:

Reversible isothermal expansion (process 1-2, constant TH with QH heat transfer to the gas).

Reversible adiabatic expansion (process 2-3, the temperature decreases from TH to TL).

Reversible isothermal compression (process 3-4, constant TL with heat transfer from the gas).

Reversible adiabatic compression (process 4-1, temperature increases from TL to TH).

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The Figure corresponds to the Carnot cycle operating for a thermal machine, but all the processes can be reversed to study the refrigerating machine. In this second case, the cycle remains exactly the same, except that the directions of any interaction of heat and work are reversed. Heat is absorbed in a quantity QL from the low temperature reservoir, and heat is discarded in the amount of QH in a high temperature reservoir, for which a work input is required.

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A thermal machine that operates in a Carnot cycle is called a reversible machine. With this type of machine you get the maximum performance. No thermal machine that works between two given sources can have a performance superior to that of a Carnot machine that works between the same sources.

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