A monoatomic idea gas expands at constant pressure, with heat $Q$ supplied. The fraction of $Q$ which goes as work done by the gas is
Medium
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As we use
$\Delta Q=n C_{p} \Delta T$
$\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}$
From first law of thermodynamics
$\Delta Q=\Delta U+\Delta W$
$\Delta \mathrm{W}=\Delta Q+\Delta \mathrm{U}$
$\Delta \mathrm{W}=\mathrm{nR} \Delta \mathrm{T}$
As $\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$
$\frac{\Delta W}{\Delta Q}=\frac{n R \Delta T}{n C_{P} \Delta T}=\frac{R}{C_{P}}=\frac{R}{\frac{5}{2} R}=\frac{2}{5}$
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