Question

When a monoatomic gas expands at a constant pressure, what percentage of heat supplied is used to increase the internal energy of the gas?

Answer 1

For a monoatomic gas,
$C_v=\frac{3R}{2}$ and $C_p=\frac{5R}{2}$
So,
$\Delta Q=n{C}_p\Delta T=n\frac{5R}{2}\Delta T$
and $\Delta U=n{C}_v\Delta T=n\frac{3R}{2}\Delta T$
Percentage of heat required to increase internal energy $=\frac{\Delta U}{\Delta Q}\times 100=\frac{\frac{3nR\Delta T}{2}}{\frac{5nR\Delta T}{2}}\times 100$
$=60\%$