Hydrogen gas is filled in a balloon at $20^\circ C$. If the temperature is increased to $40^\circ C$ while the pressure remains constant,what fraction of the original Hydrogen gas will escape from the balloon?

Two spherical vessels of equal volume $V$ are connected by a narrow tube. The apparatus contains an ideal gas at $1 \text{ atm}$ and $300 \text{ K}$. Now,if one vessel is immersed in a bath of constant temperature $600 \text{ K}$ and the other in a bath of constant temperature $300 \text{ K}$,then the common pressure will be ...... $\text{atm}$.

In a process,the pressure of an ideal gas varies with volume as $P = \frac{a}{1 + (V/b)^2}$,where $a$ and $b$ are constants. What is the temperature of the gas when the volume of $1$ mole of the gas is $V = b$?

The temperature of an open room of volume $30\ m^3$ increases from $17^\circ C$ to $27^\circ C$ due to sunshine. The atmospheric pressure in the room remains $1 \times 10^5\ Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating,then $n_f - n_i$ will be:

If in a given container there is a gas of mass $M$ and $M_{0}$ is its molar mass,then what will be the number of moles?

For an ideal gas with pressure $P$,temperature $T$,and volume $V$,where the mass of each molecule is $m$,what is the density of the gas? ($k$ is the Boltzmann constant)