Project ForgeOne kg of an ideal gas (gas constant R = 400 J/kg·K; specific heat at constant volume Cv = 1000 J/kg·K) at 1 bar and 300 K is contained in a sealed rigid cylinder. During an adiabatic process, 100 kJ of work is done on the system by a stirrer. The increase in entropy of the system is __________ J/K.
Explanation
Rigid + adiabatic: Q=0, and work done ON the system by the stirrer means W (done BY system) = -100 kJ. ΔU = Q-W = 0-(-100) = 100 kJ. Since V is constant, ΔU = mCvΔT → 100000 = 1×1000×ΔT → ΔT=100K, so T2=400K. Entropy change for constant volume: ΔS = mCv·ln(T2/T1) = 1000×ln(400/300) = 1000×0.2877 ≈ 287.7 J/K.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
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