The temperature of an open room of volume $30\ m^3$ increases from $17^\circ C$ to $27^\circ C$ due to sunshine. The atmospheric pressure in the room remains $1 \times 10^5\ Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating,then $n_f - n_i$ will be:

$A$ gas is heated through $1\,^{\circ}C$ in a closed vessel. Its pressure is increased by $0.5\%$. The initial temperature of the gas is ...... $^{\circ}C$.

$A$ long cylindrical pipe of radius $20 \,cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When a $50 \,kg$ mass is attached to the piston,it moves down. If the air in the enclosure is cooled from temperature $T$ to $T-\Delta T$,the piston moves back to its original position. Then $\Delta T / T$ is close to (Assuming air to be an ideal gas,$g=10 \,m/s^2$,atmospheric pressure is $10^5 \,Pa$)

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

For a gas,as shown in the $P-T$ graph,the densities at points $A$ and $B$ are $\varrho_0$ and $\frac{4}{3} \varrho_0$ respectively. The value of $Y$ on the pressure $(P)$ axis is

$A$ gas is collected over water at $25^{\circ}C$. The total pressure of the moist gas was $735 \, mm$ of mercury. If the aqueous vapour pressure at $25^{\circ}C$ is $23.8 \, mm$,then the pressure of the dry gas is..... $mm$.