$50 \, cal$ of heat is required to raise the temperature of $1 \, mol$ of an ideal gas from $20^{\circ} C$ to $25^{\circ} C$,while the pressure of the gas is kept constant. The amount of heat required to raise the temperature of the same gas through the same temperature range at constant volume is ........ $cal$ $(R = 2 \, cal / mol \cdot K)$.

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively,then

When $40 \ J$ of heat is absorbed by a monatomic gas,the increase in the internal energy of the gas is (in $J$)

The ratio of specific heats $\left(\frac{C_{P}}{C_{V}}\right)$ in terms of degree of freedom $(f)$ is given by

$C_{v}$ 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

One mole of an ideal monatomic gas requires $210 \, J$ of heat to raise the temperature by $10 \, K$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by $10 \, K$,then the heat required is ....... $J$.