The equation of state for $2 \ g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be:

When the pressure of a gas is increased by $0.4\%$,its temperature increases by $1\,^{\circ}\text{C}$. What is the initial temperature of the gas?

The expansion of unit mass of a perfect gas at constant pressure is shown in the diagram. Here

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.

At constant temperature,increasing the pressure of a gas by $5\%$ will decrease its volume by ..... $\%$

$A$ vessel has $6 \ g$ of oxygen at pressure $p$ and temperature $400 \ K$. $A$ small hole is made in it so that oxygen leaks out. How much oxygen has leaked out if the final pressure is $\frac{p}{2}$ and final temperature is $300 \ K$ (in $g$)?