$A$ sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T,$ the mass of each molecule is $m.$ The expression for the density of gas is ($k =$ Boltzmann's constant)

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 $^{\circ}C$)

The temperature of a gas having $2.0 \times 10^{25}$ molecules per cubic meter at $1.38 \text{ atm}$ (Given,$k = 1.38 \times 10^{-23} \text{ J K}^{-1}$) is: (in $\text{ K}$)

If the pressure of an ideal gas contained in a closed vessel is increased by $0.5\%,$ the increase in temperature is $2 \, K.$ The initial temperature of the gas is ...... $^\circ C$

$A$ volume $V$ and pressure $P$ diagram was obtained from state $1$ to state $2$ when a given mass of a gas is subjected to temperature changes. During this process the gas is

An ideal gas is heated from $27^{\circ}C$ to $627^{\circ}C$ at constant pressure. If initial volume of gas is $4 \text{ m}^3$, then the new volume of the gas will be (in $\text{ m}^3$)