$A$ 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 $2.5 \times 10^6 \, N/m^2$?

Consider a $1 \, cm^3$ sample of air at absolute temperature $T_0$ at sea level and another $1 \, cm^3$ sample of air at a height where the pressure is one-third atmosphere. The absolute temperature $T$ of the sample at that height is

Two containers $C_{1}$ and $C_{2}$ of volumes $V$ and $4V$ respectively,hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in $C_{1}$ and $C_{2}$ are $p$ and $5p$,respectively. Heat baths are employed to maintain the temperatures in the containers at $300 \, K$ and $400 \, K$,respectively. The valve is now opened. Select the correct statement.

The $P-T$ graph shows a gas being heated. During this process from point $1$ to $2$,the volume of the gas:

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/2$ is given by the straight line

$A$ pressure cooker contains air at $1$ atm and $30^\circ C$. If the safety valve of the cooker blows when the inside pressure $\ge 3$ atm,then the maximum temperature of the air inside the cooker can be .... $^\circ C$.