The heat energy supplied to a diatomic gas at constant pressure is $210 \mathrm{~J}$, then the work done by…

The heat energy supplied to a diatomic gas at constant pressure is $210 \mathrm{~J}$, then the work done by the gas is
  1. $60 \mathrm{~J}$
  2. $150 \mathrm{~J}$
  3. $90 \mathrm{~J}$
  4. $210 \mathrm{~J}$

Solution

Heat $Q=210 \mathrm{~J}$ For diatomic $\begin{aligned} & C_V=\frac{5}{2} R \\ & C_P=R+C_v \\ & =R+\frac{5}{2} R=\frac{7}{2} R\end{aligned}$ Heat, $\mathrm{Q}=\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}=210$ $\frac{7}{2} \mathrm{R} \Delta \mathrm{T}=210$ $R \Delta T=60$ Work done by the gas, $\mathrm{W}=\mathrm{P} \Delta \mathrm{V}$ $=\mathrm{R} \Delta \mathrm{T}=60 \mathrm{~J}$

Asked in: AP EAMCET 2023 (16 May Shift 1)

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