An ideal gas has a molar heat capacity at constant pressure $C_p=2.5R$. What is the atomicity of the gas?

Solution

1. Given the molar heat capacity at constant pressure $C_p=2.5R$, we use the relation $C_v=C_p-R$ to find $C_v=1.5R$.
2. Calculate the adiabatic index $$\begin{array}{rl}\gamma & =\frac{C_p}{C_v}\\ & =\frac{2.5R}{1.5R}\\ & =\frac{5}{3}\approx 1.67\end{array}$$.
3. A value of $\gamma =1.67$ corresponds to a diatomic gas.
4. Hence the answer is (B).