For a certain gas,the ratio of specific heats is given to be $\gamma = 1.5$. For this gas,

Molar specific heat at constant volume,for a non-linear triatomic gas is (vibration mode neglected).

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:

$Assertion :$ 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.

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)?

If $\frac{R}{C_v} = 0.67$,identify the gas.