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Question

70 calorie of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 40o C to 45o C.
Find the amount of heat required to raise the temperature of the same gas through the same range at constant volume:
[R = 2 cal/mol-K]

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Solution

Given :
T1=40oC
T2=45oC
n=2

ΔT=T2T1=4540=5

Heat supplied at constant pressure

Qp=nCpΔT

70=2×Cp×5

Cp=7 cal/molK

Using CpCv=nR

where R=2 cal/molK

7Cv=2×2

Thus Cv=3 cal/molK

Heat supplied at constant volume

Qv=nCvΔT

Qv=2×3×5=30 cal

Hence, the amount of heat required to raise the temperature of the same gas through the same range at constant volume is 30 cal

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