The quantity of heat required to raise the temperature of one mole of a monoatomic gas by one degree Kelvin at constant volume is

$A$ 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

The correct relation between the degree of freedom $f$ and the ratio of specific heat $\gamma$ is

When an ideal diatomic gas is heated at constant pressure,the fraction of the heat utilized to increase the internal energy of the gas is

Match the $\frac{C_{P}}{C_{v}}$ ratio for ideal gases with different types of molecules:

Molecule type	$\frac{C_{P}}{C_{v}}$
$A$. Monoatomic	$I$. $\frac{7}{5}$
$B$. Diatomic rigid molecules	$II$. $\frac{9}{7}$
$C$. Diatomic non-rigid molecules	$III$. $\frac{4}{3}$
$D$. Triatomic rigid molecules	$IV$. $\frac{5}{3}$

When $5 \ mol$ of oxygen gas is heated at constant volume from $10^{\circ}C$ to $20^{\circ}C$,the change in internal energy is ........ $cal$. (Given: $C_P = 8 \ cal/mol \cdot K$,$R = 2 \ cal/mol \cdot K$)