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=T2−T1=45−40=5Heat supplied at constant pressure Qp=nCpΔT ∴ 70=2×Cp×5⟹Cp=7 cal/mol−KUsing Cp−Cv=nRwhere R=2 cal/mol−K⟹ 7−Cv=2×2 Thus Cv=3 cal/mol−KHeat supplied at constant volume Qv=nCvΔT⟹Qv=2×3×5=30 calHence, 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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