In a certain process, the pressure of an ideal gas varies with volume according to the relation $P=\frac{a}{\{1+{\left(\frac{V}{b}\right)}^2\}}$, where $a$and $b$ are constants. When the volume of one mole of gas is $V= b$, the temperature of the gas will be,

In the figure, the volume of container $X$ is double of the volume of container $Y$. Both are filled with ideal gas. The temperature of $X$ is $200 \mathrm{K}$ and that of $Y$ is $400 \mathrm{K}$. If the mass of gas in $X$ is $m$, then the mass of gas in $Y$ will be?

Two identical glass bulbs are interconnected by a thin glass tube at $0 \text{°C}$. A gas is filled in these bulbs. If one bulb is placed in ice and another bulb is placed in hot bath, the pressure of the gas become $1.5$ times. The temperature of hot bath will be.

Pressure versus temperature graph of an ideal gas is as shown in figure. Density of the gas at point $A$ is ${\rho }_0$. Density at point $B$ will be: