The quantity $\frac{PV}{kT}$ represents ($k=$ Boltzmann 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 .......

Air is pumped into an automobile tube up to a pressure of $200\, kPa$ in the morning when the air temperature is $22^{\circ}C$. During the day,the temperature rises to $42^{\circ}C$ and the tube expands by $2\%$. The pressure of the air in the tube at this temperature will be approximately ...... $kPa$.

Explain why the air pressure in a car tire increases while the car is in motion.

Two containers $C_{1}$ and $C_{2}$ of volumes $V$ and $4V$ respectively,hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in $C_{1}$ and $C_{2}$ are $p$ and $5p$,respectively. Heat baths are employed to maintain the temperatures in the containers at $300 \, K$ and $400 \, K$,respectively. The valve is now opened. Select the correct statement.

$O_2$ gas is filled in a cylinder. If the pressure is doubled and the temperature is quadrupled,what will be the factor by which the density changes?