THE SECOND LAW OF THERMODYNAMICS
Kelvin Planck’s statement: It is impossible to construct a device that, operating continuously, will produce no effect other than transfer of heat from a single thermal reservoir and performance of an equal amount of work.The term thermal reservoir refers to a very large system in stable equilibrium, to which or from which, any amount of heat can be transferred at constant temperature.
A thermal reservoir supplying heat continuously at constant temperature is known as source. (Example: Sun)
A thermal reservoir receiving heat continuously at constant temperature is known as sink. (Examples: River, Sea)
From Kelvin-Planck statement it is clear that for any system to operate in a cycle and to give out work continuously it should interact with a minimum of two reservoirs at different temperatures. The system will receive heat from the high temperature reservoir and reject heat to the low temperature reservoir. Such devices are known as heat engines. Performance (or) Efficiency of a heat engine can be expressed as the ratio of desired output to the required input. In a heat engine the desired output is net work output and the required input is total heat input.
From first law of thermodynamics
Clausius statement: Unaided by an external agency heat can not be transferred from a body at lower temperature to a body at higher temperature.
Devices that are used to transfer heat from a body at lower temperature to a body at higher temperature are known as refrigerators (or) heat pumps. If the high temperature side is atmosphere it is a refrigerator. If the low temperature side is atmosphere it is known as a heat pump. The performance index here is called coefficient of performance (COP). In refrigerator (and heat pumps) the performance is the ratio of two independent parameters and hence the possibility of getting the value more than unity is always there. But the term efficiency is restricted to a maximum of unity. Hence the term efficiency is not used here.
Figure- Refrigerator
Figure - Heat Pump
Similarly for a heat pumps (Figure)
EQUIVALENCE OF KELVIN-PLANCK AND CLAUSIUS STATEMENTS
The Clausius and Kelvin-Planck statements of the second law are entirely equivalent. This equivalence can be demonstrated by showing that the violation of either statement can result in violation of the other one.Referring to Figure(a) the device marked Clausius violator is pumping Q1 amount of heat from a low temperature reservoir at T1 to a high temperature reservoir at T2 without the aid of any external agency. This is an impossible arrangement.
If such an arrangement is possible it would also violate Kelvin-Planck statement. Let a heat engine operating between the same reservoirs at T2 and T1 take in Q2 as heat input at T2. It converts a part of this heat into work and rejects heat Q3to the sink at T1. Since the Clausius violator is rejecting the same quantity Q2at T2, it can be supplied directly into the heat engine so that the reservoir at T2 can be eliminated. This combination as shown in Figure(b) is producing continuous work with a single reservoir at T1. Hence it violates the Kelvin-Planck statement.
Referring to Figure a Kelvin-planck violator is converting all heat QH taken from the reservoir at TH into work. If such an impossible heat engine is assumed to exist it will violate the Clausius statement. Consider a refrigerator pumping QL heat from the low temperature reservoir at TL to the reservoir at higher temperature TH. Combined with the Kelvin-Planck violator, the arrangement is pumping QL heat from TL to TH, without any external agency. Hence it violate the Clausius statement.
REVERSIBLE PROCESS
A process is said to be reversible if it can be reversed without leaving any trace on the surroundings.For example, let a system be taken from state 1 to state 2 with a work transfer of +5 kJ and heat transfer of -10 kJ. If the process is reversible, while taking the system from state 2 to state 1, the work transfer must be -5 kJ and heat transfer must be +10 kJ. So that, both the system and surroundings are returned to their initial states at the end of the process 2 to 1.
IRREVERSIBILITY AND CAUSES OF IRREVERSIBILITY
The factors that make a process irreversible are known as irreversibilities. Various forms of irreversibilities are listed below.a) Friction : Friction occurs at the interface of two bodies moving relative to each other. It is the main cause of irreversibility in many processes. Energy spent in overcoming friction is dissipated in the form of heat which can never be restored.
b) Heat transfer through finite temperature difference: Once heat is transferred from a body at higher temperature to a body at lower temperature, it can never be reversed without the aid of an external agency.c) Unresisted expansion : Consider a vessel with two chambers as given in the arrangement as shown in Fig. If the members separating the gas from vacuum is removed, gas will expand and occupy the entire space. Since the expansion has no influence on the surroundings, there is no work output in this process. But to restore the initial arrangement, a definite work input is required.
d) Mixing of two gases : Consider a vessel with two chambers, one with O2 and the other with N2. When the member separating O2 & N2 is removed, uniform mixing is taking place without any work output. But such a process can not be reversed without any work input.
e) Throttling : It is a totally irreversible process. Gas or vapour will expand through a restricted passage with its pressure decreasing rapidly without any work output. Such an expansion can not be reversed.
EXTERNALLY AND INTERNALLY REVERSIBLE PROCESS
As mentioned earlier if no irreversibility occur outside the system boundaries during the process, it is known as externally reversible.If no irreversibility occur within the boundary of the system during a process, it is known as internally reversible process. For such a process, the path of the reverse process will follow exactly that of the forward process in any property diagram.
To be totally reversible or simply reversible both external and internal reversibility must be ensured.
THE CARNOT CYCLE
In 1824, Nicholas Sadi Carnot proposed a classical ideal cycle consisting of four processes. All processes are individually reversible and hence the cycle as a whole is a reversible cycle. The processes that make up the Carnot cycle are :Process 1-2
The working substance is taken in a piston cylinder arrangement as given in Figure(a). Heat is added reversibly and isothermally from a high temperature reservoir at TH. Since the process is to be reversible, the temperature TH of the reservoir should be equal to or infinitesimally greater than that of the working substance.
Process 2-3
The working substance is allowed to expand reversibly and adiabatically until its temperature falls down to TL. The process is represented by Figure (b)
Process 3-4
Heat is rejected by the working substance to a low temperature reservoir kept TL or at temperature infinitesimally smaller than TL.
Process 4-1
The working substance is then compressed reversibly and adiabatically until its temperature becomes TH and the cycle continues.
The cycle has been represented in a p-V diagram in Figure. The included area represents the net work done in the cycle. From first law of thermodynamics net work done is equal to net heat transfer in the cycle. Since QH is the heat added to system and QL is the heat rejected by the system, the neat heat transfer is QH - QL.
It shows that efficiency of Carnot engine is purely a function of TH and TL.
Since the Carnot cycle being completely reversible, if carried out in reverse direction, the magnitudes of all energy transfers remain the same but their sign change. This reversed Carnot cycle can be applied for a refrigerator or a heat pump. Figure 4.10 shows the p-V diagram of a reversed Carnot cycle.
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