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For a monoatomic gas, the work done at constant pressure is ' $\mathrm{W}$ '. The heat supplied at constant…
For a monoatomic gas, the work done at constant pressure is ' $\mathrm{W}$ '. The heat supplied at constant volume for the same rise in temperature of the gas is
$2 \mathrm{~W}$ W $\frac{\mathrm{W}}{2}$ $\frac{3 \mathrm{~W}}{2}$ Solution
At constant pressure, $\mathrm{W}=\mathrm{P} . \Delta \mathrm{V}$
For an ideal gas, $\mathrm{PV}=\mathrm{nRT}$
$\begin{aligned}
& \therefore \mathrm{P} \Delta \mathrm{V}=\mathrm{n} \mathrm{R} \Delta \mathrm{T} \\
& \mathrm{W}=\mathrm{n} \mathrm{R} \Delta \mathrm{T}
\end{aligned}$
Heat supplied at constant volume,
$\begin{aligned}
& \mathrm{Q}=\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{n} \frac{3 \mathrm{R}}{2} \Delta \mathrm{T} \\
& \quad\left(\text { Formonoatomic gas } \mathrm{C}_{\mathrm{v}}=\frac{3}{2} \mathrm{R}\right) \\
& \therefore \mathrm{Q}=\frac{3 \mathrm{~W}}{2}
\end{aligned}$
Asked in: MHT CET 2021 (23 Sep Shift 1)
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