• # question_answer 2 moles of a mono-atomic gas undergo isobaric expansion as shown in figure. The efficiency for the process is found to be $\frac{x}{10}$. Find the value of$x$. A) 2 B) 3 C) 4 D) 5

 [c] Work done by gas $={{P}_{0}}(2{{V}_{0}}-{{V}_{0}})={{P}_{0}}{{V}_{0}}$          ...(i) Heat input to the gas = Work done + Change in internal energy
 $={{P}_{0}}{{V}_{0}}+\frac{f}{2}nR\Delta T$ $={{P}_{0}}{{V}_{0}}+\frac{3}{2}(nR{{T}_{f}}-nR{{T}_{i}})$ $={{P}_{0}}{{V}_{0}}+\frac{3}{2}(2{{P}_{0}}{{V}_{0}}-{{P}_{0}}{{V}_{0}})$ $\therefore$    Heat input $=\frac{5}{2}{{P}_{0}}{{V}_{0}}$   ....(ii) Efficiency $=\frac{\text{Work}\,\text{done}}{\text{Heat}\,\text{inpup}}$ $=\frac{{{P}_{0}}{{V}_{0}}}{\frac{5}{2}{{P}_{0}}{{V}_{0}}}=\frac{2}{5}$ Efficiency $=\frac{4}{10}=\frac{x}{10}\Rightarrow \,x=4$