Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

If $\alpha$ and $\beta$ are the volume and pressure coefficients respectively of an ideal gas, then

$A$ large flask contains air at $27 \, ^{\circ}C$. In order to expel half the mass of air from the flask, the flask should be heated up to what temperature in $^{\circ}C$?

$A$ gas is filled in a vessel at a pressure given by $P = (6.02 \times 10^{23})kT$,where $k$ is the Boltzmann constant and $T$ is the absolute temperature. The number of molecules per unit volume of the gas is:

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

$A$ 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 $\,m$)?