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3.107 A helium gas is heated at constant volume from a state of 100 kPa, 300 K to 500 K. A following process expands the gas at constant pressure to three times the initial volume. What are the specific work and the specific heat transfer in the combined process? The two processes are: N 1 - 2: Constant volume V2 = V1 P. 2 - 3: Constant pressure P3 = P2 P 1 V Use ideal gas approximation for helium. State 1: T, P = v| =RT,/PI State 2: V2 = V1 = P2 = P1 (T2/T1 ) State 3: P3 = P2 = V3 = 3V2; T3 = T2 V3/V2 = 500 x 3 = 1500 K We find the work by summing along the process path. 1W3 = 1W2 + 2W3 = 2W3 = P3(V3 - V2) = R(T3 - T2) = 2.0771 kJ/kg-K x (1500 - 500) K = 2077 kJ/kg 193 = U3 - U1 + 1W3 = Cv (T3 - T1) + 1W3 = 3.116 kJ/kg-K x (1500 - 300) K + 2077 kJ/kg = 5816 kJ/kg