According to the law of equipartition of energy, the molar specific heat of a diatomic gas at constant volume, where the molecule has one additional vibrational mode, is:

Which one of the following is $NOT$ a correct expression for an ideal gas?
[$C_{P}=$ Molar specific heat of a gas at constant pressure,
$C_{V}=$ Molar specific heat of a gas at constant volume,
$\gamma=$ Ratio of two specific heats of a gas,$R=$ Universal gas constant]

$A$ cylinder of fixed capacity $67.2 \text{ litres}$ contains helium gas at $STP$. The amount of heat needed to raise the temperature of the gas in the cylinder by $20^{\circ} C$ is: (in $\text{ J}$)

$5 \ \text{moles}$ of an unknown gas is heated at constant volume from $10^\circ \text{C}$ to $20^\circ \text{C}$. The molar specific heat of this gas at constant pressure is $c_p = 8 \ \text{cal/mol} \cdot ^\circ \text{C}$ and the gas constant is $R = 8.36 \ \text{J/mol} \cdot ^\circ \text{C}$. The change in the internal energy of the gas is . . . . . . calorie.

If $C_P$ and $C_V$ are the specific heats of unit mass of nitrogen at constant pressure and constant volume respectively,then:

For hydrogen gas $(H_2)$,$C_P - C_V = a$,and for oxygen gas $(O_2)$,$C_P - C_V = b$. What is the relationship between $a$ and $b$?