If the density of the Sun is $1.4 \, g \, cm^{-3}$, the pressure is $1.4 \times 10^9 \, \text{atm}$, and the molar mass of the gas in the Sun is $2 \, g \, mol^{-1}$, then the temperature of the Sun will be: [Take $R = 8.4 \, J \, mol^{-1} \, K^{-1}$]

$A$ 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..... $mm$.

$A$ balloon contains $500 \ m^3$ of helium at $27^{\circ}C$ and $1 \ atm$ pressure. The volume of the helium at $-3^{\circ}C$ temperature and $0.5 \ atm$ pressure will be ..... $m^3$.

$A$ cylinder contains $10\, kg$ of gas at a pressure of $10^7\, N/m^2$. The quantity of gas taken out of the cylinder,if the final pressure is $2.5 \times 10^6\, N/m^2$,will be ..... $kg$ (Temperature of the gas is constant).

An ideal gas undergoes a process maintaining the relation between pressure $(P)$ and volume $(V)$ as $P = P_o(1 + (\frac{V_o}{V})^2)^{-1}$,where $P_o$ and $V_o$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_o$ and $3V_o$ respectively undergo the above-mentioned process,calculate the difference in the temperatures of these samples,$T_B - T_A$,assuming the process is evaluated at their initial states. ($R$ = gas constant)

An air bubble of volume $1.0 \; cm^{3}$ rises from the bottom of a lake $40 \; m$ deep at a temperature of $12 \; ^{\circ}C$. To what volume (in $cm^{3}$) does it grow when it reaches the surface,which is at a temperature of $35 \; ^{\circ}C$?