$A$ closed compartment containing gas is moving with some acceleration in a horizontal direction. Neglect the effect of gravity. Then the pressure in the compartment is

One mole of the ideal gas goes through the process $p=p_0\left[1-\alpha\left(\frac{V}{V_0}\right)^3\right]$,where $p$ and $V$ are pressure and volume,$p_0, V_0$ and $\alpha$ are constants. If the maximum attainable temperature of the gas is $\left(\frac{3}{4}\right) \frac{p_0 V_0}{R}$,then the value of $\alpha$ is

The cross-sectional area of a piston is $8 \times 10^{-3} \, m^2$. The gas has a temperature of $300 \, K$,a pressure of $1.0 \times 10^5 \, Pa$,and a volume of $2.4 \times 10^{-3} \, m^3$. When the gas is heated by a heater,the piston moves by $0.1 \, m$. If the spring constant is $8000 \, N/m$,find the final temperature in $K$.

Initially,a gas of diatomic molecules is contained in a cylinder of volume $V_{1}$ at a pressure $P_{1}$ and temperature $250\, K$. Assuming that $25\%$ of the molecules get dissociated,causing a change in the number of moles. The pressure of the resulting gas at temperature $2000\, K$,when contained in a volume $2V_{1}$,is given by $P_{2}$. The ratio $\frac{P_{2}}{P_{1}}$ is:

$A$ flat plate is moving normal to its plane through a gas under the action of a constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

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.