The average force applied on the wall of a closed container depends as $T^{x}$ where $T$ is the temperature of an ideal gas. The value of $x$ is

Which of the following shows the correct relationship between the pressure $P$ and density $\rho$ of an ideal gas at constant temperature?

At constant pressure,the ratio of the increase in volume of an ideal gas per degree rise in Kelvin temperature to its original volume is $(T =$ absolute temperature of the gas$)$

$A$ container $AB$ in the shape of a rectangular parallelepiped of length $5 \,m$ is divided internally by a movable partition $P$ as shown in the figure. The left compartment is filled with a given mass $m$ of an ideal gas of molar mass $M_1 = 32$ while the right compartment is filled with an equal mass $m$ of another ideal gas of molar mass $M_2 = 18$ at the same temperature. What will be the distance of $P$ from the left wall $A$ when equilibrium is established (in $\,m$)?

For an ideal gas at constant pressure,if the volume is $V$ at a temperature of $27^{\circ}C$,what will be its final volume when the temperature is increased to $327^{\circ}C$?

$A$ sample of oxygen gas and a sample of hydrogen gas both have the same mass,same volume,and the same pressure. The ratio of their absolute temperatures is (Molecular weights of $O_2$ and $H_2$ are $32$ and $2$ respectively).