GITAM, Department of Engineering Physics

# Change of Entropy in a Reversible process

 Let us consider a complete reversible process – a Carnots Cycle ABCD as shown in figure. In the isothermal expansion from A to B, the working substance absorbs  an amount of heat Q1 at a constant temperature T1 of the source. When heat is absorbed by the system, Q1 is positive, and hence entropy change is positive because T is positive. Hence

gain in entropy from A-to-B = Q1/T1.          -------------------- (1)

Ie, source loses this heat Q1 at temperature T1: so its entropy decreases by Q1/T1.

During the adiabatic expansion from B-to-C, there is no change in entropy (since heat is neither taken nor given out).

During the isothermal compression from C-to-D, the working substance gives out a quantity of heat Q2 at a constant temperature T2 of sink and so the

loss in entropy from C-to-D = Q2/T2           -------------------- (2)

ie, the sink gains this heat Q2 at T2, so its entropy increases by Q2/T2.

Again during the adiabatic compression from D-to-A there is no change in entropy.

It means that the total change in entropy of the working substance in a complete cycle of a reversible process is zero. Simmilarly the change in entropy of the combined system of source and sink is also zero. Thus in a cycle of reversible process, the entropy of the system remains unchanged or the change in entropy of the system is zero.

Change of entropy in an irreversible process

Consider an irreversible process such as conduction or radiation of heat. Let a system consist of two bodies at temperatures T1 and T2. Since heat always flows from higher to lower temperature, both by conduction and radiation, let Q be the quantity of heat thus transmitted.

-   Decrease in entropy of hotter body

-   Increase in entropy of colder body

-   Net change in entropy of the system

Which is a positive quantity since T1>T2. we may, therefore, generalize the result and say that the entropy of the system increases in all irreversible processes.

Note: Since a reversible process represents a limiting ideal case, all actual processes are inherently irreversible. It means, ie., cycle after cycle of operation is performed, the entropy of the system increases and tends to a maximum value. This is the principle of increase of entropy and pay be stated as “the entropy of an isolated system either remains constant or increases according as the processes it undergoes are irreversible or reversible”. Analytically it may be expressed as dS ³ 0.