Project ForgeConsider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume cᵥ is equal to 750 J·kg⁻¹·K⁻¹. A stirrer performs 225 kJ of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be __________ bar (in integer).
Explanation
The container is insulated (Q=0) and rigid (no boundary work), but the stirrer does 225 kJ of work ON the gas, so by sign convention W=−225 kJ. ΔU = Q−W = 0−(−225) = +225 kJ. ΔT = ΔU/(m·cᵥ) = 225000/(1×750) = 300 K, so T₂=600 K. Since volume is constant, pressure scales with temperature (ideal gas): P₂ = P₁×(T₂/T₁) = 1×(600/300) = 2 bar.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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