For two different gases $X$ and $Y$, having degrees of freedom $f_1$ and $f_2$ and molar heat capacities at constant volume $C_{V1}$ and $C_{V2}$ respectively, the $\ln P$ versus $\ln V$ graph is plotted for an adiabatic process, as shown.

One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points $(V_{0}, T_{0})$ and $(2 V_{0}, 3 T_{0})$ in a $V-T$ diagram. What is the value of the heat capacity of the gas at the point $(V_{0}, T_{0})$?

$A$ vessel containing nitrogen gas is supplied a heat of $498 \,J$, so as to raise the temperature of the gas by $40^{\circ} C$ at constant pressure. The mass of nitrogen gas in the vessel is (Molecular mass of nitrogen $= 28 \,g/mol$; Universal gas constant $= 8.3 \,J \,mol^{-1} \,K^{-1}$) (in $\,g$)

In the kinetic theory of gases,which of the following statements regarding elastic collisions of the molecules is wrong?

$A$ thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and it is suddenly brought to rest. Assuming no heat is lost to the surroundings,its temperature increases by

As per the kinetic theory of gases, which of the following statements is/are true?
$(a)$ Temperature of a gas is a measure of the average kinetic energy of a molecule.
$(b)$ Temperature of a gas depends on the nature of the gas.
$(c)$ Heavier molecules have lower average speed.
$(d)$ Lighter molecules have lower average speed.