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Question

A vessel of volume 0.2m3 contains hydrogen gas at temperature 300K and pressure 1bar. Find the heat required to raise the temperature to 400K. The molar heat capacity of hydrogen at constant volume is 5cal/molK.

A
(ΔQ)v=2.1kcal
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B
(ΔQ)v=4.2kcal
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C
(ΔQ)v=2kcal
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D
(ΔQ)v=4kcal
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Solution

The correct option is D (ΔQ)v=4kcal
As here volume of gas remains constant, we get
(ΔQ)v=μCvΔT
Here, Cv=5cal/molK
And ΔT=(400300)=100K
And so for ideal gas PV=μRT
μ=(10)5×(0.2)8.31×300=8mol
(ΔQ)v=8×5×100=4kcal

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