When $300 \ J$ of heat is given to an ideal gas with $C_{p} = \frac{7}{2} R$, its temperature rises from $20^{\circ}C$ to $50^{\circ}C$ while keeping its volume constant. The mass of the gas is (approximately) . . . . . . g. (Assume the molar mass of the gas is $28 \ g/mol$ and $R = 8.314 \ J/mol \cdot K$).

$C_{v}$ 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

$A$ gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume $(C_v)$ to the specific heat of gas at constant pressure $(C_p)$ will be.

$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).
$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.

For a gas,the difference between the two specific heats is $4150 \ J/kg \ K$. What is the specific heat at constant volume of the gas if the ratio of specific heats is $1.4$ (in $J/kg \ K$)?

The ratio of specific heats $(\gamma)$ of an ideal gas is given by