$A$ cylinder contains $10 \, kg$ of gas at a pressure of $10^7 \, N/m^2$. What amount of gas in $kg$ must be removed so that the final pressure becomes $2.5 \times 10^6 \, N/m^2$?

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

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 ...... $\text{atm}$.

$A$ flask containing air at $27\,^{\circ}C$ at atmospheric pressure is corked up. $A$ pressure of $2.5\,atm$ would force the cork out. The temperature at which it happens is

The volume of a gas at $21^{\circ}C$ temperature and $768 \,mm$ pressure is $1 \,L$. If the density of the gas is $1.2 \,g/L$ at $NTP$,then its mass will be ..... $g$.

An air bubble of volume $1.0 \; cm^{3}$ rises from the bottom of a lake $40 \; m$ deep at a temperature of $12 \; ^{\circ}C$. To what volume (in $cm^{3}$) does it grow when it reaches the surface,which is at a temperature of $35 \; ^{\circ}C$?