The Carnot Cycle

Externally and internally reversible processes

As mentioned earlier if no irreversibilities occur outside the system boundaries during the process, it is known as externally reversible.

If no irreversibilities 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 reversibilities must be ensured.

4.7     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 4.8(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 4.8(b)

Process 3-4

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 4.9. The included area represents the net work done in the cycle. From first law of thermodynamics net workdone 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.

Where

                                    Q_L = 3W4 + U4 - U3

Since the process is isothermal U4 = U3

                    \  QL  =  3W4

                               =  P3 V3 ln

                               =  mRTL ln 

        Similarly  QH  =  mRTH ln 

                Substituting the above condition we get

 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.