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 is suddenly broght to rest. Assuming no heat is lost to the surroundings, its temperature increases by

Two gases$A$ and $B$ are contained in the same vessel which is at temperature $T$. The number of molecular of gas $A$ is $N$ and mass of each molecule is $m$. The number of molecules of gas $B$ is $2\ N$ and mass of its each molecules is $2\ m$. If mean square velocity of $x$ of gas $B$ is $v^2$ and mean square velocity of $x$ component of velocity of molecules of gas $A$ is $u_x^2$ then ${{u_x^2}}/{{{v^2}}}$  is

A gas mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is

The value of critical temperature in terms of van der Waals' constants $a$ and $b$ is given by

At ….. $K$ temperature is the $rms$ velocity of a hydrogen molecule equal to that of an oxygen molecules at $47^o\  C$ ?