Write the value of $\frac{C_P}{C_V}$ for a monoatomic gas.

$70 \, cal$ of heat are required to raise the temperature of $2 \, moles$ of an ideal gas at constant pressure from $30^{\circ}C$ to $35^{\circ}C$. The amount of heat required to raise the temperature of the same gas through the same range ($30^{\circ}C$ to $35^{\circ}C$) at constant volume is ..... $cal$ $(R = 2 \, cal/mol \cdot K)$.

For a monoatomic gas,the work done at constant pressure is $W$. For the same rise in temperature of the gas,the heat supplied at constant volume is:

$Assertion:$ At a given temperature,the specific heat of a gas at constant pressure $(C_p)$ is always greater than its specific heat at constant volume $(C_v)$.
$Reason:$ When a gas is heated at constant volume,some extra heat is needed compared to that at constant pressure for doing work in expansion.

The specific heat capacities of an ideal gas at constant pressure and at constant volume are $620 \ J \ kg^{-1} \ K^{-1}$ and $420 \ J \ kg^{-1} \ K^{-1}$ respectively. The density of the gas at $STP$ is approximately, (in $kg \ m^{-3}$)

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