$A$ gas is enclosed in a closed pot. On keeping this pot in a train moving with high speed,the temperature of the gas

Assertion $(A):$ The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and volume.
Reason $(R):$ The molecules of gas collide with each other and the velocities of the molecules change due to the collision.

Which graph represents the variation of $PV$ with $V$ for a fixed mass of an ideal gas at constant temperature?

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Statement $I$: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v(T_f - T_i) = \frac{nR}{\gamma - 1}(T_f - T_i)$, where $\gamma = C_p/C_v, T_i = $ initial temperature, $T_f = $ final temperature. Statement $II$: Relation between degree of freedom $f$ and $\gamma(= C_p/C_v)$ is $\gamma = 1 + \frac{2}{f}$. Choose the correct answer from the options given below.

In the isothermal expansion of $10\,g$ of gas from volume $V$ to $2V$,the work done by the gas is $575\,J$. What is the root mean square speed of the molecules of the gas at that temperature (in $m/s$)?