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

Air pressure in a car tyre increases during driving. Explain.

$A$ vessel has $8 \ g$ of oxygen at pressure $P$ and temperature $400 \ K$. $A$ small hole is made in it so that oxygen leaks out. How many grams of oxygen leak out if the final pressure is $P/4$ and the temperature is $200 \ K$?

An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston of cross-section $8.0 \times 10^{-3} \, m^2$. Initially,the gas is at $300 \, K$ and occupies a volume of $2.4 \times 10^{-3} \, m^3$,and the spring is in its relaxed state as shown in the figure. The gas is heated by a small heater until the piston moves out slowly by $0.1 \, m$. The force constant of the spring is $8000 \, N/m$ and the atmospheric pressure is $1.0 \times 10^5 \, N/m^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless,and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible.) (in $, K$)

According to Charles' law, what is the possible minimum temperature?

$A$ closed vessel contains $8\,g$ of oxygen and $7\,g$ of nitrogen. The total pressure is $10\,atm$ at a given temperature. If oxygen is now absorbed by introducing a suitable absorbent,the pressure of the remaining gas in $atm$ will be: