Question

At very high temperature vibrational degrees also becomes active. At such temperature an ideal diatomic gas has a molar specific heat at constant pressure $C_P=?$

• A. $\frac{3}{2}R$
• B. $\frac{5}{2}R$
• C. $\frac{6}{2}R$
• D. $\frac{9}{2}R$

Answer 1

Answer: (D)

$\frac{9}{2}R$

Due to translation, there would be 3 degrees of freedom.

Due to rotation there would be 2 more degrees of freedom for the diatomic molecule.

Due to vibration there would be 2 more degrees of freedom.

Thus $f=7$

$C_V=\frac{f}{2}R=\frac{7}{2}R$

$⟹C_P=C_V+R=\frac{9}{2}R$