Two vessels $A$ and $B$ are of the same size and are at the same temperature. Vessel $A$ contains $1 \ g$ of hydrogen and vessel $B$ contains $1 \ g$ of oxygen. If $P_{A}$ and $P_{B}$ are the pressures of the gases in $A$ and $B$ respectively,then the ratio $\frac{P_{A}}{P_{B}}$ is:

$A$ 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 $\,m$)?

The pressure and temperature of an ideal gas in a closed vessel are $720 \, kPa$ and $40^\circ C$ respectively. If $\frac{1}{4}^{th}$ of the gas is released from the vessel and the temperature of the remaining gas is raised to $353^\circ C$,the final pressure of the gas is ....... $kPa$.

Air pressure in a car tyre increases during driving. Explain.

Which of the following graphs represents the behavior of an ideal gas? Symbols have their usual meaning.

We have a jar filled with gas characterized by parameters $P, V, T$ and another jar $B$ filled with gas having parameters $2P, V/4, 2T$,where symbols have their usual meaning. The ratio of the number of molecules in jar $A$ to those in jar $B$ is