At a constant temperature,by what percentage $(\%)$ must the pressure of a given mass of gas be increased so that its volume decreases by $10\%$ (in $.1$)?

The air density at Mount Everest is less than that at the sea level. It is found by mountaineers that for one trip lasting a few hours,the extra oxygen needed by them corresponds to $30,000 \, cc$ at sea level (pressure $1 \, atm$,temperature $27^{\circ}C$). Assuming that the temperature around Mount Everest is $-73^{\circ}C$ and that the oxygen cylinder has a capacity of $5.2 \, L$,the pressure at which $O_2$ must be filled (at site) in the cylinder is .... $atm$.

There are two vessels filled with an ideal gas where the volume of one is double the volume of the other. The large vessel contains the gas at $8 \ kPa$ at $1000 \ K$,while the smaller vessel contains the gas at $7 \ kPa$ at $500 \ K$. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at $600 \ K$,at steady state the pressure in the vessels will be (in $kPa$).

What is a mole? Write two equations for a mole.

Dry air at sea level contains $75.5\%\, N_2$ by mass. If the total atmospheric pressure is $1 \,atm$,the partial pressure of nitrogen is approximately $... \,atm$.

$A$ 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 $10^5 \,Pa$):