Question

The specific heats $C_P$ and $C_V$ , of a diatomic gas $A$ are $29Jmo{l}^{-1}{K}^{-1}$ and $22Jmo{l}^{-1}{K}^{-1}$ respectively. Another diatomic gas $B$ , has the corresponding values as $30Jmo{l}^{-1}{K}^{-1}$ and $21Jmo{l}^{-1}{K}^{-1}$ respectively. Which among the following is correct?

• A. $A$ has one vibrational degree of freedom and $B$ has two vibrational degrees of freedom
• B. $A$ has one vibrational degree of freedom and $B$ has zero vibrational degree of freedom
• C. $A$ and $B$ both have one vibrational degree of freedom
• D. $A$ and $B$ both have two vibrational degrees of freedom

Answer 1

Answer: (B)

If $f$ is the degree of freedom of a gas molecule, then
$\frac{C_P}{C_V}=\left(\frac{f+2}{f}\right){\left(\frac{C_P}{C_V}\right)}_A=\frac{29}{22}=\left(\frac{f_A+2}{f_A}\right)\Rightarrow f_A=6{\left(\frac{C_P}{C_V}\right)}_B=\frac{30}{21}=\left(\frac{f_A+2}{f_A}\right)\Rightarrow f_B=5$
So $A$ has one vibrational degree of freedom and $B$ has none