The number of air molecules in a $(5 \,m \times 5 \,m \times 4 \,m)$ room at standard temperature and pressure is of the order of

$A$ gas has a volume $V$ at a temperature of $27^{\circ}C$. If the temperature is increased to $327^{\circ}C$ while keeping the pressure constant,what will be the new volume of the gas?

What is Avogadro number? Write its value.

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......

One mole of an ideal gas undergoes a process in which pressure $P$ varies with volume $V$ as $P = 3 - g \left(\frac{V}{V_0}\right)^2$, where $V_0$ and $g$ are constants. The maximum temperature attainable by the ideal gas during this process is ($All$ quantities are in $SI$ units and $R$ is the gas constant).

$A$ fixed amount of gas has a volume $V$ at constant pressure. If the temperature of the gas is increased such that the $v_{rms}$ of the molecules doubles,then its new volume will be .......