The pressure-temperature graph for an ideal gas is shown in the figure. At point $A$,the density of the gas is $\rho_0$. What will be the density at point $B$?

The temperature of a gas having $2.0 \times 10^{25}$ molecules per cubic meter at $1.38 \text{ atm}$ (Given,$k = 1.38 \times 10^{-23} \text{ J K}^{-1}$) is: (in $\text{ K}$)

Molar volume is the volume occupied by $1 \; mol$ of any (ideal) gas at standard temperature and pressure ($STP$: $1 \; atm$ pressure,$0^{\circ} C$). Show that it is $22.4 \; L$.

An open glass tube is immersed in mercury such that a length of $8 \ cm$ extends above the mercury level. The open end of the tube is then closed and sealed,and the tube is raised vertically by an additional $46 \ cm$. What will be the length of the air column above the mercury in the tube now? (Atmospheric pressure = $76 \ cm$ of $Hg$)

$A$ perfect gas of a given mass is heated first in a small vessel and then in a large vessel,such that their volumes remain unchanged. The $P-T$ curves are

How much should the pressure be increased in order to reduce the volume of a given mass of gas by $5 \%$ at a constant temperature (in $\%$)?