[emeraldcrystal]

[Donaldson Tan]

Work done by the gas
= integration from V_initial to V_final P dV
= integration from V_initial to V_final {nRT/V} dV

This is an isoentropic process involving a perfect gas,
=> PV^γ = Constant
=> Given that P = nRT/V, then (nRT/V)V^γ = Constant
=> TV^γ-1 = Constant/nR = Constant K for a fixed mass of gas.
=> T = K/V^γ-1

K = T_initialV_initial^γ-1

Hence, work done by gas
= integration from V_initial to V_final {nRT/V} dV
= integration from V_initial to V_final (nR/V)*(K/V^γ-1) dV
= integration from V_initial to V_final (nRK/V^γ) dV

[listerineman]

But doesn't that equation for work only apply to an isothermal process? This equation is for a constant temperature.
= integration from Vinitial to Vfinal {nRT/V} dV