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Question

Gaseous hydrogen contained initially under standard conditions in a sealed vessel of volume V=5L was cooled by ΔT=55K. What amount of heat will be lost by the gas (in Joules) ?

A
255
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B
255
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C
200
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D
200
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Solution

The correct option is A 255
By the first law of thermodynamics
ΔQ=ΔU+ΔW
Here ΔW=0 as the volume remains constant.
ΔQ=ΔU
Now ΔU=nCv(ΔT)
=nRγ1ΔT (asCv=Rγ1)
We have PoV=nRT0
or
nR=PoVTo
Thus we get
ΔU=1.013×105×(5×103)×55273(1.41)=255J

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