An ideal mono-atomic gas is taken through a process such that $dQ = 3dU$. The molar heat capacity for this process is: (in $R$)

The specific heat at constant pressure $(C_P)$ is greater than the specific heat at constant volume $(C_V)$ for the same gas because:

The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. Its density $\rho$ at $N.T.P.$ will be: [Where $P$ and $T$ are pressure and temperature respectively at $N.T.P.$]

$Assertion :$ 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.

If the molar specific heat at constant volume is $\frac{3R}{2}$,then the adiabatic index $\gamma$ is:

Using the law of equipartition of energy, the specific heat (in $J\, kg^{-1}\, K^{-1}$) of aluminium at room temperature can be estimated to be (atomic weight of aluminium $= 27$).