$A$ thermally insulated vessel with nitrogen gas at $27^{\circ} C$ is moving with a velocity of $100 \ m/s$. If the vessel is stopped suddenly,then the percentage change in the pressure of the gas is nearly (assume entire loss in $KE$ of the gas is given as heat to gas and $R=8.3 \ J \ mol^{-1} \ K^{-1}$)

The average translational kinetic energy of a molecule in a gas is $E_1$. The kinetic energy of an electron $(e)$ accelerated from rest through a potential difference of $V$ volts is $E_2$. The temperature at which $E_1 = E_2$ is possible (assuming the mass of the molecule and electron are the same) is: (where $N$ is Avogadro's number, $e$ is the elementary charge, $R$ is the gas constant)

$N$ molecules each of mass $m$ of gas $A$ and $2N$ molecules each of mass $2m$ of gas $B$ are contained in the same vessel at temperature $T$. The mean square of the velocity of molecules of gas $B$ is $v^2$ and the mean square of $x$ component of the velocity of molecules of gas $A$ is $w^2$. The ratio $\frac{w^2}{v^2}$ is

$A$ piston is slowly pushed into a metal cylinder containing an ideal gas. Which of the following statements is/are incorrect?

The number of air molecules per $cm^3$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is $.........$

$A$ certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity $v$. The molecular mass of the gas is $M$. What is the rise in temperature of the gas when the vessel is suddenly stopped? (Given $\gamma = C_P/C_V$)