A polyatomic gas has f vibrational degrees of freedom, then the ratio of the specific heat at constant pressure to that at constant volume will be

Question

A polyatomic gas has f vibrational degrees of freedom, then the ratio of the specific heat at constant pressure to that at constant volume will be (A) (4+f/3+f) (B) (4-f/3-f) (C) (3+f/4+f) (D) (3-f/4-f)

Tardigrade Admin · Accepted Answer

For a polyatomic atom value of specific heat at constant volume,

C_{V} = (3 + f) R

where,

f =

vibration degree of freedom and

R =

gas constant.
Now,

C_{p} = C_{V} + R

C_{p} = (3 + f) R + R

C_{p} = (4 + f) R

Now, ratio of

C_{p}

and

C_{V}

\frac{C _{p}}{C _{V}} = \frac{4 + f}{3 + f}

Q. A polyatomic gas has $f$ vibrational degrees of freedom, then the ratio of the specific heat at constant pressure to that at constant volume will be

$\frac{4 + f}{3 + f}$

$\frac{4 - f}{3 - f}$

$\frac{3 + f}{4 + f}$

$\frac{3 - f}{4 - f}$

For a polyatomic atom value of specific heat at constant volume, $C_{V} = (3 + f) R$
where, $f =$ vibration degree of freedom and $R =$ gas constant.
Now, $C_{p} = C_{V} + R$
$C_{p} = (3 + f) R + R$
$C_{p} = (4 + f) R$
Now, ratio of $C_{p}$ and $C_{V}$
$\frac{C _{p}}{C _{V}} = \frac{4 + f}{3 + f}$

Q. A polyatomic gas has f vibrational degrees of freedom, then the ratio of the specific heat at constant pressure to that at constant volume will be

3+f4+f​

3−f4−f​

4+f3+f​

4−f3−f​