In this article we will discuss about:- 1. Introduction to Reversibility and Irreversibility 2. Carnot Engine and Carnot Cycle 3. Carnot Theorem 4. Reversible Cycle.
Introduction to Reversibility and Irreversibility:
Quasi—means nearly or almost. So, quasi-static process means nearly static process or a process which proceeds with extreme slowness. A quasi-static process proceeds from one equilibrium state to another equilibrium state till the end of process. All the states passed through by the system, during the process are all equilibrium states.
A quasi-static process is represented on the PV-diagram by a continuous curve and if we carry out the process in the reverse direction, then it is possible to retrace the same path. Hence it is known as a Reversible process.
Whereas in case of Irreversible process only end states are equilibrium states and all the intermediate states are non-equilibrium states and is represented by means of a dotted curve.
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Conditions of Reversibility or Factors Making the Process Irreversible:
(i) A process should be quasi-static
(ii) There should be no friction
(iii) Both the system and the surroundings should restore their initial state after the process is reversed.
Carnot Engine and Carnot Cycle:
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Carnot, a French Engineer, was the first to introduce the concept of reversible cycle. Carnot devised an engine, which is named after him as Carnot engine. Carnot engine works between high temperature and low temperature reservoirs.
Carnot engine works on Carnot cycle. It consists of an alternate series of two reversible isothermal and two reversible adiabatic processes. Since each process is reversible, the Carnot cycle as a whole is reversible.
Carnot cycle (Figs 3.12 and 3.13) is independent of nature of working fluid. It can work with any working substance like gas, vapour or any other working substance. Let us assume that the working fluid of the engine is a gas.
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Figure 3.12 shows the proposed reversible engine working between source at T1 and sink at T2. It consists of a cylinder, which has a piston working in it without friction. The walls of the cylinder and piston are assumed to be perfect insulators of heat. The cylinder head is so arranged that it can be a perfect conductor and perfect insulator alternatively.
During the beginning of the stroke the cylinder head is made perfect conductor and the heat source at T1 is brought in contact with the gas in the cylinder. The gas expands isothermally at T1 from state point (1) to state point (2). During the expansion process, heat supplied Q1 is used in the expansion of the gas.
Process 1-2:
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It is an Isothermal expansion process.
Law for the process is PV = C
Pressure falls from P1 to P2
Volume increases from V1 to V2 and, T =C.
Note:
For derivation refer Ideal gases work done during an Isothermal process.
When the state point (2) is reached, the cylinder head is made perfect insulator and the gas in the cylinder is allowed to expand till the end of the stroke by following PVγ = C.
Process 2-3:
It is an adiabatic expansion process.
Pressure falls from P2 to P3
Volume increases from V2 to V3
Temperature falls from T1 to T2
For an adiabatic process Q = 0.
Now after expansion stroke, its compression stroke starts. During this cylinder head is made perfect conductor and the system is brought in contact with the sink at T2 and the gas is now compressed isothermally from state point (3) to state point (4). During this process work is done on the gas.
It is an Isothermal compression process.
Pressure increases from P3 to P4
Volume decreases from V3 to V4 and T2 = C
–ve sign implies work is done on the gas during compression.
For isothermal process Q = W
Again the cylinder head is made perfect insulator and the gas is compressed adiabatically to state point (1).
Process 4-1:
It is an adiabatic compression process.
Pressure increases from P4 to P1
Volume decreases from V4 to V1
Temperature increases from T2 to T1
Note:
Carnot cycle is a reversible cycle. If the processes are carried out in anticlockwise direction then it will work as heat pump.
For all the four process, the cycle will be completed when the isothermal expansion and isothermal compression ratios are same.
The proof for this is given below:
From the diagram we get –
Carnot Theorem:
Two cyclic heat engines EA and EB operating between the same source and sink out of which EB is reversible (Fig. 3.15).
Carnot’s theorem states that “No engine operating between two thermal reservoirs can have an efficiency more than that of a Carnot’s engine operating between the same two reservoirs”.
That is “Carnot’s engine will be more efficient than any other engine operating between the same temperature reservoirs “.
Let two heat engines EA and EB operate between the source at temperature T1 and the sink at temperature T2 as shown in Fig. 3.15.
Let EA be any irreversible engine and EB be any reversible heat engine. We have to prove that the efficiency of EB is more than that of EA. Now, let us assume that this is not true and η A is greater than η B. Let the rates of heat transfer are such that,
Note:
Here the magnitudes of heat and work quantities will remain the same, but their directions will be reversed as shown in Fig. 3.16.
Since WA > WB, some part of WA (equal to WB) may be fed to drive the reversed heat engine EB.
Since Q1A = Q1B = Q1 the heat discharged by EB (reversed heat engine B) may be supplied to EA. The source may therefore be eliminated as shown in the Fig. 3.17.
The net result is that EA and EB together will constitute a heat engine, which operating in a cycle, produces, network (WA – WB) while exchanging heat with a single reservoir at T2.
Thus violates the Kelvin Planck’s statement of the second law. Hence the assumption than hA > hB is wrong.
∴ ηB ≥ ηA
Reversible Cycle:
If a process can occur in a reverse order, and if the initial state all energies transferred or transformed during the process can completely be restored in both system and environment, the process is called reversible.
If a process is really reversible, then no after effects or changes are evident in the system or in the environment when the process occurs in the forward and then in the reverse direction.
An irreversible process that is not reversible. A quasi-static process implies an infinitely slow process since all potential differences acting on the system are infinitesimally small. Such a process may be thought of as an infinite succession of equilibrium states.
It may be stopped at any time and made to proceed in the opposite direction, thereby reversing the original process in every detail and restoring the system and environment to its original state.
We know that the thermodynamic cycle is defined as a cyclic process end states of which are same. If all the processes in a cycle are reversible process, then the cycle is called a reversible cycle.
Reversible process and consequently reversible cycle is an ideal one. There are no losses in the form of friction, temperature differences for heat transfer to take place. Presence of fraction makes the process mechanically irreversible and the temperature difference for heat transfer during the process makes the process thermally irreversible. Therefore reversible cycle is an ideal cycle.
Engines working on reversible cycle are called reversible engines:
(a) No heat engine operating in cycles between two reservoirs at different temperatures can have a greater efficiency than a reversible engine operating between the same two reservoirs and
(b) All reversible engines operating between two reservoirs at given temperatures have the same efficiency.
Carnot cycle is a reversible cycle and its efficiency depends only on the temperature.
In reversible engines, heat is received while the working substance is at the same constant temperature as the source and heat is rejected while the working substance is at the same constant temperature as the sink.