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Q.
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 ?
The heat $Q$ is converted into the internal energy and work. According to the first law of thermodynamics,
$Q = U + W$
$ \Rightarrow nC _{ p } \Delta t = n C _{ v } \Delta t + W$
$\frac{W}{Q}=\frac{n C_{p} \Delta t-n C_{v} \Delta t}{n C_{p} \Delta t} $
$\frac{c_{p}-c_{v}}{c_{p}}=1-\frac{1}{\gamma}$
$=1-\frac{1}{\frac{5}{3}}=\frac{2}{5}$