(c)Using the equation: ds= do CdT+Pdv The entropy change of the gas in going form point (1)to point (3)is AS=l dS 厂+y一cm+m 4Po 3R +RIn_3R In 4+ rin 2 R 8315×(1.5×1.37+0.69)=2282(J/K) d) The entropy change and the internal energy change of the gas in going form point(1)to point ( 3) are zero, since they are state variables(c) Using the equation: T C T P V T Q S d V d d d + = = The entropy change of the gas in going form point (1) to point (3) is 8.315 (1.5 1.37 0.69) 22.82(J/K) ln 4 ln 2 2 2 3 ln 4 ln 2 3 ln ln d d d 0 0 0 0 0 0 1 3 1 3 3 1 3 1 3 1 = × × + = = + = + ∆ = = + = + ∫ ∫ ∫ R R V V R R PV R PV R V V R T T C V V R T C T S S V V V T T V (d) The entropy change and the internal energy change of the gas in going form point (1) to point (3) are zero, since they are state variables