The molar heat capacity at constant volume for a monatomic gas is

A
$(3 / 2) R$
B
$(5 / 2) R$
C
$(7 / 2) R$
D
$(9 / 2) R$

Solution:

For a monatomic gas, $C_{V, m} = (3 / 2) R$

In a monoatomic gas, each atom has 3 degrees o freedoms. They are of translation type. They contribute to the heat capacity.
N atoms of a monoatomic gas has 3N degrees of freedom.
Hence,
$\begin{array}{l} C_{V} = (\frac{\partial U}{\partial T}) \\ = \frac{3}{2} {NK}_{B} \\ = \frac{3}{2} nR \end{array}$
The molar heat capacity is $\frac{C_{V, m}}{n} = 32 R$

Solution:

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