We have a sample of gas characterized by $P, V$ and $T$ and another sample of gas characterized by $2P, V/4$ and $2T$. What is the ratio of the number of molecules in the first and second samples (in $: 1$)?

Under constant temperature,the graph between $P$ and $1/V$ is:

The lowest pressure (the best vacuum) that can be created in the laboratory at $27^{\circ}C$ is $10^{-11} \; mm$ of $Hg$. At this pressure,the number of ideal gas molecules per $cm^{3}$ will be:

When air is pumped into a cycle tyre, the volume and pressure of the air in the tyre both increase. What about Boyle's law in this case?

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

If the density of the Sun is $1.4 \, g \, cm^{-3}$, the pressure is $1.4 \times 10^9 \, \text{atm}$, and the molar mass of the gas in the Sun is $2 \, g \, mol^{-1}$, then the temperature of the Sun will be: [Take $R = 8.4 \, J \, mol^{-1} \, K^{-1}$]