Question

When an ideal diatomic gas is heated at a constant pressure, then what fraction of heat energy is used to increase the internal energy of the gas system?

Answer 1

Change in internal energy, $dU=n{C}_{v}dT$
At a constant pressure, heat energy, $dQ=n{C}_{p}dT$
Therefore, $\frac{dU}{dQ}=\frac{n{C}_{v}dT}{n{C}_{p}dT}=\frac{C_v}{C_p}=\frac{1}{\gamma }$

For a diatomic gas, $\gamma =\frac{7}{5}$
So, $\frac{dU}{dQ}=\frac{5}{7}$