The equation of an ideal gas in terms of pressure $(P)$,absolute temperature $(T)$,and density $(d)$ is:

Inside a cylinder having insulating walls and closed at ends is a movable piston,which divides the cylinder into two compartments. On one side of the piston is a mass $m$ of a gas and on the other side a mass $2m$ of the same gas. What fraction of the total volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? Consider that the movable piston is conducting so that the temperature is the same throughout.

$A$ sample of $O_2$ gas has a volume of $100 \ ml$ at a pressure of $1 \ atm$ and a temperature of $27^{\circ}C$. If the pressure is increased to $2 \ atm$ while the volume remains $100 \ ml$,the new temperature will be .... $^{\circ}C$.

An ideal gas at pressure $P$ and temperature $T$ is enclosed in a vessel of volume $V$. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to $P^{\prime}$. Assuming that the temperature of the gas remains constant during the leakage,the number of moles of the gas that have leaked is

Three containers of the same volume contain three different gases. The masses of the molecules are $m_1, m_2$ and $m_3$ and the number of molecules in their respective containers are $N_1, N_2$ and $N_3$. The gas pressures in the containers are $P_1, P_2$ and $P_3$ respectively. All the gases are now mixed and put in one of the containers. The pressure $P$ of the mixture will be

$A$ container of fixed volume contains a gas at $27^{\circ} C$. To double the pressure of the gas,the temperature of the gas should be raised to . . . . . . ${ }^{\circ} {C}$.