$A$ balloon contains $1500 \ m^3$ of $He$ at $27^{\circ} C$ and $4 \ atm$ pressure. The volume of $He$ at $-3^{\circ} C$ temperature and $2 \ atm$ pressure will be: (in $m^3$)

Equal masses of $N_2$ and $O_2$ gases are filled in containers $A$ and $B$ respectively. The volume of container $B$ is twice the volume of container $A$. What is the ratio of the pressure in container $A$ to that in container $B$?

An engineer is given a fixed volume $V_m$ of metal with which to construct a spherical pressure vessel. Assuming the vessel has thin walls and is pressurized to its bursting point,the amount of gas the vessel can contain,$n$ (in moles),depends only on $V_m$ $(m^3)$,the temperature $T$ $(K)$,the ideal gas constant $R$ $(J/(K \cdot mol))$,and the tensile strength of the metal $\sigma$ $(N/m^2)$. Which of the following gives $n$ in terms of these parameters?

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

What is the universal gas constant? Write its value and unit.

According to Charles' law, what is the possible minimum temperature?