A certain amount of heat energy is supplied to a monoatomic ideal gas which expands at constant pressure. What fraction of the heat energy is converted into work ?

Suppose \(Q\) amount of heat is supplied to monoatomic gas which expands at constant pressure. This heat is then converted into the internal energy and work. According to the first law of thermodynamics,
\(Q=U+W\)
\(\text {or } \quad n C_{p} \Delta T=n C_{V} \Delta T+W\)
where, \(C_{p}\) and \(C_{V}\) are the specific heat capacity at constant pressure and volume, respectively.
\(\therefore\) The fraction of heat converted to work is given as
\(\frac{W}{Q}=\frac{n C_{p} \Delta T-n C_{V} \Delta T}{n C_{p} \Delta T}\)
For monoatomic gas, \(n=1\)
\(\Rightarrow \frac{W}{Q}=\frac{C_{p}-C_{V}}{C_{p}} =\frac{\frac{5}{2} R-\frac{3}{2} R}{\frac{5}{2} R} \)
\( =\frac{R}{\frac{5}{2} R}=\frac{2}{5}\)