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Question

# 70 cal of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30∘ C to 35∘ C. The amount of heat required to raise the temperature of the same gas through same range of temperature (30∘ C to 35∘ C) at constant volume is Given (γ=7/5)

A
30 cal
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B
50 cal
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C
70 cal
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D
90 cal
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Solution

## The correct option is B 50 calHeat absorbed at constant pressure to increase the temperature by ΔT, Qp=nCpΔT ...(i) Cp=molar heat capacity at constant pressure ⇒Heat required to raise the temperature of same gas by ΔT at constant volume is, QV=nCVΔT ...(ii) CV=molar heat capacity at constant volume ⇒QVQp=CVCp QV=Qp×CVCp QV=70×1γ ∴QV=70×57=50 cal

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