The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is

Work done by an ideal daitomic gas is given by, $$\begin{gathered} W=∆Q-∆U \\ ∆Q=n{C}_p∆T where C_p for diatomic gas is \frac{5}{2}R \\ ∆U=n{C}_v∆T where C_v for diatomic gas is \frac{3}{2}R \\ hence W=n\frac{5}{2}R∆T-n\frac{3}{2}R∆T=nR∆T\left(\frac{5}{2}-\frac{3}{2}\right)=nR∆T \end{gathered}$$

And heat supplies is given by, $(∆Q{)}_p=n{C}_p∆T=n\frac{5}{2}R∆T$

Hence the ratio is given by$\frac{∆\mathrm{W}}{{\left(∆\mathrm{Q}\right)}_{\mathrm{P}}}=\frac{nR∆T}{n{\displaystyle \frac{5}{2}}R∆T}$

                                           $\frac{∆\mathrm{W}}{{\left(∆\mathrm{Q}\right)}_{\mathrm{P}}}=\frac{2}{5}$