Which of the following graphs correctly represents the variation of $\beta = - (dV/dP)/V$ with $P$ for an ideal gas at constant temperature?

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

When air is filled in a balloon, both the pressure and volume increase while the temperature remains constant. Why is Boyle's law not obeyed in this case?

At a room temperature of $23^{\circ}C$,a person inhales $1500 \, ml$ of air at a body temperature of $37^{\circ}C$. If the pressure and mass remain constant,what will be the volume of the air in the person's lungs in $ml$?

State the Avogadro hypothesis.

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