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 ...... $kPa$.

One mole of an ideal gas undergoes a process $P = \frac{2V^2}{1+V^2} \, Pa$. The change in temperature of the gas when the volume changes from $V = 1 \, m^3$ to $V = 2 \, m^3$ is:

Find the ratio of the density of air at the top of a mountain to the density of air at the bottom of the mountain,given the conditions shown in the image.

Consider a $1 \, cm^3$ sample of air at absolute temperature $T_0$ at sea level and another $1 \, cm^3$ sample of air at a height where the pressure is one-third atmosphere. The absolute temperature $T$ of the sample at that height is

The tyre of a motor car contains air at $15^{\circ} C$. If the temperature increases to $35^{\circ} C$, the approximate percentage increase in pressure is (ignore the expansion of the tyre).

$A$ cylinder containing gas at $27\,^{\circ}C$ is divided into two parts of equal volume,each $100\,cm^3$,and at equal pressure by a piston of cross-sectional area $10.85\,cm^2$. The gas in one part is raised in temperature to $100\,^{\circ}C$ while the other is maintained at the original temperature. The piston and walls are perfect insulators. How far will the piston move during the change in temperature? (in $cm$)