Question

The specific heats $C_{P}$ and $C_{V}$ , of a diatomic gas $A$ are $29 \, J \, mol^{- 1}K^{- 1}$ and $22 \, J \, mol^{- 1}K^{- 1}$ respectively. Another diatomic gas $B$ , has the corresponding values as $30 \, J \, mol^{- 1}K^{- 1}$ and $21 \, J \, mol^{- 1}K^{- 1}$ 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