Kinetic Theory

JEE Main level, numerical answer, medium

86 of 168

Question 86 of 168

A monoatomic gas performs a work of Q4\dfrac{Q}{4} where QQ is the heat supplied to it. The molar heat capacity of the gas will be _____ RR during this transformation.
Where RR is the gas constant.

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Answer: 2

Using first law of thermodynamics,
Q=∆U+WQ=∆U+W
⇒Q=ΔU+Q4\Rightarrow Q=\Delta U+\dfrac{Q}{4}
⇒ΔU=3Q4\Rightarrow \Delta U=\dfrac{3Q}{4}
⇒∆U=32nRΔT=3Q4\Rightarrow ∆U=\dfrac{3}{2}nR\Delta T=\dfrac{3Q}{4}
Therefore, molar heat capacity, C=Qn∆TC=\dfrac{Q}{n∆T}
⇒C=2R\Rightarrow C=2R

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