An ideal gas is initially at temperature $T$ and volume $V.$ Its volume is increased by $\Delta V$ due to an increase in temperature $\Delta T,$ pressure remaining constant. The quantity $\delta = \Delta V / (V \Delta T)$ varies with temperature as

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 $\text{ K}$)

$A$ cylinder of volume $30 \, L$ contains oxygen at an initial gauge pressure of $15 \, atm$ and a temperature of $27^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$. The mass of oxygen taken out of the cylinder is approximately ........ $kg$. (Given: $R = 8.31 \, J \, mol^{-1} K^{-1}$,molar mass of $O_2 = 32 \, g/mol$ or $32 \times 10^{-3} \, kg/mol$)

At what temperature does the volume of an ideal gas at $0^{\circ}C$ become triple? (in $^{\circ}C$)

$A$ 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 $^{\circ}C$?

$A$ 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