A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the…
A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy is
$30 \%$
$40 \%$
$50 \%$
$60 \%$
Solution
For a monoatomic gas,
$\gamma=\frac{C_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3}$
We know $\Delta \mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}$ and $\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}$
$\frac{\Delta U=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{~T}}{\Delta \mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{~T}}=\frac{\mathrm{C}_{\mathrm{V}}}{\mathrm{C}_{\mathrm{P}}}=\frac{3}{5}$
$\therefore \quad$ The percentage of total heat used in changing the internal energy is $\frac{3}{5} \times 100=60 \%$.