$A$ bicycle tyre is filled with air having pressure of $270\,kPa$ at $27^{\circ}C$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ}C$ is $............kPa$.

Two spherical vessels of equal volume $V$ are connected by a narrow tube. The apparatus contains an ideal gas at $1 \text{ atm}$ and $300 \text{ K}$. Now,if one vessel is immersed in a bath of constant temperature $600 \text{ K}$ and the other in a bath of constant temperature $300 \text{ K}$,then the common pressure will be ...... $\text{atm}$.

The expansion of unit mass of a perfect gas at constant pressure is shown in the diagram. Here

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $B$ in the $V-T$ graph. Then the expansion of the same ideal gas of mass $2m$ at a pressure $2P$ is given by the straight line:

$A$ thin tube sealed at both ends is $100 \ cm$ long. It lies horizontally, the middle $20 \ cm$ containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced? (Given: cross-section of the tube can be assumed to be uniform) ........ $cm$

What is the number of oxygen molecules in a cylinder of volume $1 \ m^3$ at $27^{\circ}C$ and $13.8 \ Pa$? (Boltzmann constant $k = 1.38 \times 10^{-23} \ JK^{-1}$)