An ideal gas is filled in a closed container and the container is moving with uniform acceleration in the horizontal direction. Neglect gravity. The pressure inside the container is ...............

Given below are two statements:
Statement $I$: The temperature of a gas is $-73^{\circ} C$. When the gas is heated to $527^{\circ} C$,the root mean square speed of the molecules is doubled.
Statement $II$: The product of pressure and volume of an ideal gas is equal to the translational kinetic energy of the molecules.
In the light of the above statements,choose the correct answer from the options given below:

Two gases of equal mass are in thermal equilibrium. If $P_a, P_b$ and $V_a, V_b$ are their respective pressures and volumes,then which relation is true?

$A$ monoatomic gas of mass $4.0 \, g$ is kept in an insulated container. The container is moving with a velocity of $30 \, m/s$. If the container is suddenly stopped,then the change in temperature of the gas (where $R$ is the gas constant) is given by $\frac{x}{3R}$. The value of $x$ is ..........

$A$ very tall vertical cylinder is filled with a gas of molar mass $M$ under isothermal conditions at temperature $T$. The density and pressure of the gas at the base of the container are $\rho_0$ and $p_0$,respectively. Choose the correct statement$(s)$ if gravity is assumed to be constant throughout the container.

An insulated system contains $4$ moles of an ideal diatomic gas at temperature $T$. When a heat $Q$ is supplied to the gas,$2$ moles of the gas is dissociated into atoms and the temperature remains constant. Then the relation between $Q$ and $T$ is ($R=$ universal gas constant.)