What is Boltzmann's constant?

In a process,the pressure of an ideal gas varies with volume as $P = \frac{a}{1 + (V/b)^2}$,where $a$ and $b$ are constants. What is the temperature of the gas when the volume of $1$ mole of the gas is $V = b$?

$A$ balloon contains $500 \ m^3$ of helium at $27^{\circ}C$ and $1 \ atm$ pressure. The volume of the helium at $-3^{\circ}C$ temperature and $0.5 \ atm$ pressure will be ..... $m^3$.

For a monoatomic gas at constant pressure,the $V \rightarrow T$ graph is . . . . . .

An air bubble of volume $2.9 \ cm^3$ rises from the bottom of a swimming pool $5 \ m$ deep. At the bottom of the pool,the water temperature is $17^{\circ} C$. The volume of the bubble when it reaches the surface,where the water temperature is $27^{\circ} C$,is . . . . . . $cm^3$. ($g = 10 \ m/s^2$,density of water $\rho = 10^3 \ kg/m^3$,and $1 \ atm = 10^5 \ Pa$)

$A$ vessel has $6 \ g$ of oxygen at pressure $p$ and temperature $400 \ K$. $A$ small hole is made in it so that oxygen leaks out. How much oxygen has leaked out if the final pressure is $\frac{p}{2}$ and final temperature is $300 \ K$ (in $g$)?