Thermodynamics

JEE Main level, single correct, medium

53 of 190

Question 53 of 190

nn moles of an ideal gas with constant volume heat capacity Cv{C}_{v} undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is:

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Answer: (C) nRCv+nR\dfrac{nR}{{C}_{v}+nR}

From First Law of thermodynamics,
ΔQ=ΔU+Δw\Delta Q=\Delta U+\Delta w
ΔwΔQ=1−ΔUΔQ=1−ncvΔTncpΔT\dfrac{\Delta w}{\Delta Q}=1-\dfrac{\Delta U}{\Delta Q}=1-\dfrac{n{c}_{v}\Delta T}{n{c}_{p}\Delta T}
=1−cvR+cv=1-\dfrac{{c}_{v}}{R+{c}_{v}}
=RR+cv=\dfrac{R}{R+{c}_{v}}
As, ncv=Cvn{c}_{v}={C}_{v}
ΔwΔQ=nRCv+nR\dfrac{\Delta w}{\Delta Q}=\dfrac{nR}{{C}_{v}+nR}

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