Air is filled at $60^{\circ} C$ in a vessel of open mouth. The vessel is heated to a temperature $t^{\circ} C$ so that $\frac{1}{4}$th of the air escapes from the vessel. Assuming air as an ideal gas and the volume of the vessel remains constant, the value of '$t$' is: (in $^{\circ} C$)

The tyre of a bicycle has a volume of $2 \times 10^{-3} \ m^3$. Initially,the tube is filled to $75 \%$ of its volume with air at an atmospheric pressure of $10^5 \ N \ m^{-2}$. When a rider is on the bicycle,the area of contact of the tyre with the road is $24 \times 10^{-4} \ m^2$. The mass of the rider with the bicycle is $120 \ kg$. If a pump delivers a volume of $500 \ cm^3$ of air in each stroke,then the number of strokes required to inflate the tyre is $(g = 10 \ m \ s^{-2})$.

The volume-temperature graph at atmospheric pressure for a monoatomic gas ($V$ in $m^3$,$T$ in $^{\circ}C$) is:

The given figure represents two isobaric processes for the same mass of an ideal gas. Then:

We have a sample of gas characterized by $P, V$ and $T$ and another sample of gas characterized by $2P, V/4$ and $2T$. What is the ratio of the number of molecules in the first and second samples (in $: 1$)?

An ideal gas is initially at temperature $T$ and volume $V.$ Its volume is increased by $\Delta V$ due to an increase in temperature $\Delta T,$ pressure remaining constant. The quantity $\delta = \Delta V / (V \Delta T)$ varies with temperature as