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Q.

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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a

150RJ

b

300RJ

c

75RJ

d

100RJ

answer is B.

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Detailed Solution

For 1 mol of gas, Q=CvΔT+PΔTAt constant volume, ΔV=0For 2 moles of gas, ΔU=2CvΔTFrom PV=nRT=2R×300 and  P2V=2RTf∴ Tf=150K∴ Q=2CvTf−Ti=2Cv(150−300)=−300CvJIn the next process,Q=2CpΔT=2Cp(300−150)=300CpJ∴  Net heat absorbed =−300Cv+300Cp                                            =300Cp−Cv=300RJ
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