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)

$A$ diatomic gas of molecular weight $30 \, g/mol$ is filled in a container at $27 \, ^\circ C$. It is moving at a velocity of $100 \, m/s$. If it is suddenly stopped,the rise in temperature of the gas is:

An insulated container containing a monoatomic gas of molar mass $M$ is moving with a velocity $V_{0}$. If the container is suddenly stopped,find the change in temperature.

The figure shows a plot of $PV/T$ versus $P$ for $1.00 \times 10^{-3} \; kg$ of oxygen gas at two different temperatures.
$(a)$ What does the dotted plot signify?
$(b)$ Which is true: $T_{1} > T_{2}$ or $T_{1} < T_{2}$?
$(c)$ What is the value of $PV/T$ where the curves meet on the $y$-axis?
$(d)$ If we obtained similar plots for $1.00 \times 10^{-3} \; kg$ of hydrogen,would we get the same value of $PV/T$ at the point where the curves meet on the $y$-axis? If not,what mass of hydrogen yields the same value of $PV/T$ (for the low-pressure,high-temperature region of the plot)?
(Molecular mass of $H_{2} = 2.02 \; u$,of $O_{2} = 32.0 \; u$,$R = 8.31 \; J \; mol^{-1} K^{-1}$.)

The mass of a hydrogen atom is $3.32 \times 10^{-27} \, kg$. If $10^{23}$ atoms per second strike a wall of area $2 \, cm^2$ at an angle of $45^{\circ}$ with the normal to the wall and reflect elastically with a speed of $10^3 \, m/s$,the pressure exerted on the wall will be: $(N/m^2)$

$A$ fixed mass of gas at constant pressure occupies a volume $V$. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be