The equation of state for $5 \, g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be (where $R$ is the gas constant).

One mole of a perfect gas in a cylinder fitted with a piston has a pressure $P,$ volume $V,$ and temperature $T.$ If the temperature is increased by $1 \, K$ keeping pressure constant,the increase in volume is

$A$ 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 $m^3$)

The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta P$ is applied at a constant temperature is the same as the change when the temperature is reduced by a small quantity $\Delta T$ at constant pressure. The initial temperature and pressure of the gas were $300 \ K$ and $2 \ atm$ respectively. If $|\Delta T| = C|\Delta P|$,then the value of $C$ in $(K/atm)$ is......

What does the universal gas constant $R$ represent? Write its value and unit.

What is a mole? Write two equations for a mole.