The gas law $\frac{PV}{T} = \text{constant}$ is true for

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 $R = 8.4 \, J \, mol^{-1} \, K^{-1}$]

Air is filled at $60^oC$ in a vessel with an open mouth. The vessel is heated to a temperature $T$ so that $1/4^{th}$ of the air escapes. Assuming the volume of the vessel remains constant,the value of $T$ is ....... $^oC$.

$A$ 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 other end of the piston,it moves down by a distance $\Delta l$ before coming to equilibrium. Assuming air to be an ideal gas,$\Delta l / l$ (see figure) is close to ($g=10 \,m/s^2$,atmospheric pressure is $10^5 \,Pa$):

An ideal gas at pressure $P$ and temperature $T$ is enclosed in a vessel of volume $V$. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to $P'$. Assuming that the temperature of the gas remains constant during the leakage, the number of moles of the gas that have leaked 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.