When the volume of a system is increased two times and the temperature is decreased to half of its initial temperature,then the pressure becomes ...... times.

At $100 \, K$ and $0.1 \, \text{atm}$ pressure, the volume of helium gas is $10 \, \text{litres}$. If volume and pressure are doubled, its temperature will change to ....... $K$.

Air is pumped into an automobile tube up to a pressure of $200\, kPa$ in the morning when the air temperature is $22^{\circ}C$. During the day,the temperature rises to $42^{\circ}C$ and the tube expands by $2\%$. The pressure of the air in the tube at this temperature will be approximately ...... $kPa$.

For a gas,as shown in the $P-T$ graph,the densities at points $A$ and $B$ are $\varrho_0$ and $\frac{4}{3} \varrho_0$ respectively. The value of $Y$ on the pressure $(P)$ axis is

$A$ vessel of volume $8\, L$ contains an ideal gas at $300\, K$ and $2\, atm$ pressure. The gas is allowed to leak until the pressure becomes $125\, kPa$. Calculate the number of moles that leaked out if the temperature remains constant.

The floor area of a room is $20 \, m^2$ and its walls are $3 \, m$ high. If the pressure of air in the room is $1 \, atm$ and the temperature is $27 \, ^\circ C$,find the mass of the air in the room. (Take the molar mass of air as $29 \, g/mol$). Given: $1 \, atm = 1.01 \times 10^5 \, N \, m^{-2}$,$R = 8.31 \, J \, mol^{-1} K^{-1}$.