To raise the temperature of a certain mass of gas by $50^{\circ} C$ at a constant pressure,$160$ calories of heat is required. When the same mass of gas is cooled by $100^{\circ} C$ at constant volume,$240$ calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

The amount of heat that must be supplied to $35 \ g$ of oxygen at room temperature to raise its temperature by $80^{\circ} C$ at constant volume is (molecular mass of oxygen is $32$ and $R = 8.3 \ J \ mol^{-1} \ K^{-1}$) (in $kJ$)

The ratio of the specific heats $\frac{C_{p}}{C_{v}}=\gamma$,in terms of degrees of freedom $(n)$ is

$C_{v}$ and $C_{p}$ denote the molar specific heat capacities of a gas at constant volume and constant pressure,respectively. Then
$(A)$ $C_{p}-C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
$(B)$ $C_{p}+C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
$(C)$ $C_{p} / C_{v}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
$(D)$ $C_{p} \cdot C_v$ is larger for a diatomic ideal gas than for a monoatomic ideal gas

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

The molar specific heat of an ideal gas at constant pressure and constant volume is $C_p$ and $C_v$ respectively. If $R$ is the universal gas constant and the ratio of $C_p$ to $C_v$ is $\gamma$,then $C_v$ is equal to: