Two moles of an ideal gas at $$300$$ K were cooled at constant volume so that the pressure is reduced to half the initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature. Find the total heat absorbed by the gas, if R is the gas constant.

Question

Infinity Learn · Accepted Answer

For $$1$$ mol of gas, $$Q=Cv$$Δ$$T+P$$ΔTAt constant volume, Δ$$V=0For$$ $$2$$ moles of gas, Δ$$U=2Cv$$ΔTFrom $$PV=nRT=2R$$×$$300$$ and  $$P2V=2RTf$$∴ $$Tf=150K$$∴ $$Q=2CvTf$$−$$Ti=2Cv(150$$−$$300)=$$−$$300CvJIn$$ the next process,$$Q=2Cp$$Δ$$T=2Cp(300$$−$$150)=300CpJ$$∴  Net heat absorbed $$=$$−$$300Cv+300Cp$$                                            $$=300Cp$$−$$Cv=300RJ$$

Two moles of an ideal gas at 300 K were cooled at constant volume so that the pressure is reduced to half the initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature. Find the total heat absorbed by the gas, if R is the gas constant.

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