Question

In which of the following four state changes will the “entropy change” be negative? Prove using the relevant equations. (Only verbal answer will not be accepted. It will be proved as thermodynamic calculations by using related equations).
(a) Air isothermally expanded from 6 bar pressure to 3 bar pressure
(b) Compressing the air to half its volume at constant pressure
(c) To supply constant volume of air to the air until the pressure is threefold.
(d) Air isentropically expanded from 6 bar pressure to 3 bar pressure

Answer 1

Soln (a) Glven - To constant Platbar Ti =12 P2 a 3 bar. Applying equation for entropy change & S2 -S, = (p ln I / L - R in P2 for air : Cp = 1005 KJ/kg-K R= 0.287 KJ/kg.K Cr=0.718 KT/leg.K. S2-Si a - 0-287 In 0. 1989 KJ/kg-K Sa-Si entropy is positive for case a. (6) Gluen a Presscere = constant. Pia P2 ViEV S2-S, = (plon yg + Cunha Pi S2-S,= 1.005in x 2.7 82-5, 1.005 in (0-5) 82-S, = 0.6966 kJ/kg-K Entropy change for case (b) is negatiue.

(e) Giveno - NIE VR volume a constant PIEP P28 BP. Sa-se a good cona e 0718 In = 0.718 in (3) 32-5, = 0.7888 KJ/kg. K. entropy change is positive. (d) Given :- prize Pirt = P2 Van Pia 6bar N217 6 P2 =Bbar Ee 27 2 = ( 21/144 S2-51 = Epin V₂ Vi & Cuin! IP2 P +0.718 in 0.5 Sars, = 100516214 52-5, -0 kJ/kg-K. Entropy change for an isentropic process is always zero.