One mole of an ideal monoatomic gas initially at 1200 K and 64 atm is expanded to a final state at 300 K and 1 atm. To achieve the above change, a reversible path is constructed that involve an adiaba

Question

One mole of an ideal monoatomic gas initially at 1200 K and 64 atm is expanded to a final state at 300 K and 1 atm. To achieve the above change, a reversible path is constructed that involve an adiabatic expansion in the beginning followed by an isothermal expansion to the final state. The magnitude of net work done by the gas (in cal) is

TestHub · Accepted Answer

Adiabatic to 300 K: (T 5/2 )/P = const gives P' = 64 (300/1200) 5/2 = 64/32 = 2 atm. w ad = C V Δ T = 1.5R×900 = 1350R = 2700 cal (R = 2 cal/K-mol). Isothermal 2 to 1 atm at 300 K: w = RTln2 = 600×0.6931 = 416 cal. Total = 2700+416 = 3116 cal. Ans = 3116.

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