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Question

An ideal monoatomic gas at temperature 27C and pressure 100 bar occupies 5 L volume. 5000 cal of heat is added to the system without changing the volume. Calculate the change in temperature of the gas. (Given, R=8.31 J/mol K)

A
75 K
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B
89 K
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C
83 K
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D
90 K
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Solution

The correct option is C 83 K
From Ideal gas equation,
PV=nRT
n=PVRT
=107×5×1038.31×300
[from the data given in the question]
n=0.2×100=20

For monoatomic gas,
CV=32R
=32×8.31 J/mol-K
=32×8.314.183 cal/mol K
Let ΔT be the rise in temperature
So Q=nCVΔT
ΔT=QnCV
=500020×3=83.33
83 K

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