Question

A diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?

Answer 1

If it is heated at constant pressure, the volume must increase.
Heat in = change in internal energy + work out
dQ = dU + dW
PV = n RT
Constant pressure
PdV = nR dT = work out
Change in internal energy = n Cv dT $=n\frac{5}{2}RdT$ for diatomic gas total heat required = nR dT + $\frac{5}{2}$ n RdT)
So our answer is $\frac{\left(\frac{5}{2}\right)}{(1+\frac{5}{2})}=\frac{5}{(2+5)}=\frac{5}{7}$