Question

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $T$. The total internal energy, $U$ of a mole of this gas, and the value of $\gamma\left(=\frac{ C _{ P }}{ C _{ v }}\right)$ given, respectively, by:

• A. $U =\frac{5}{2} RT$ and $\gamma=\frac{6}{5}$
• B. $U =5 RT$ and $\gamma=\frac{7}{5}$
• C. $U =5 RT$ and $\gamma=\frac{6}{5}$
• D. $U =\frac{5}{2} RT$ and $\gamma=\frac{7}{5}$

Answer 1

Answer: (D)

Total degree of freedom $=3+2=5$
$U =\frac{ nfRT }{2} \Rightarrow \frac{5 RT }{2}$
$\gamma \Rightarrow \frac{C_{ P }}{ C _{ v }} \Rightarrow 1+\frac{2}{ f } \Rightarrow 1+\frac{2}{5} \Rightarrow \frac{7}{5}$