For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $P$ respectively. Then the slope of the graph drawn between $\log_e V$ on the $X$-axis and $\log_e P$ on the $Y$-axis is

The $PV$ versus $T$ graph for equal masses of $H_2, He$,and $O_2$ is shown in the figure. Choose the correct alternative:

$A$ volume $V$ and pressure $P$ diagram was obtained from state $1$ to state $2$ when a given mass of a gas is subjected to temperature changes. During this process the gas is

$A$ container $A$ contains a gas at thermodynamic coordinates $P, V,$ and $T$. Another container $B$ contains a different gas at $2P, V/4,$ and $2T$. The ratio of the number of molecules in container $A$ to the number of molecules in container $B$ is:

When $2 \, g$ of a gas are introduced into an evacuated flask kept at $25 \, ^\circ C$,the pressure is found to be $1 \, atm$. If $3 \, g$ of another gas is added to the same flask,the pressure becomes $1.5 \, atm$. The ratio of the molecular weights of these gases will be:

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