$A$ large flask contains air at $27 \, ^{\circ}C$. In order to expel half the mass of air from the flask, the flask should be heated up to what temperature in $^{\circ}C$?

The volume of an ideal gas is $1 \, L$ and its pressure is equal to $72 \, cm$ of mercury. It is compressed isothermally until its volume becomes $900 \, cm^3$. What is the change in pressure (stress) of the gas in $cm$ of mercury?

$O_2$ gas is filled in a cylinder. If the pressure is doubled and the temperature is quadrupled,what will be the factor by which the density changes?

One mole of an ideal gas passes through a process where pressure and volume obey the relation $P = P_0 \left[ 1 - \frac{1}{2} \left( \frac{V_0}{V} \right)^2 \right]$. Here $P_0$ and $V_0$ are constants. Calculate the change in the temperature of the gas if its volume changes from $V_0$ to $2V_0$.

Two identical glass bulbs are interconnected by a thin glass tube. Initially,both bulbs are at $0^{\circ}C$. $A$ gas is filled in these bulbs. When one bulb is placed in ice $(0^{\circ}C)$ and the other bulb is placed in a hot bath,the pressure of the gas becomes $1.5$ times the initial pressure. The temperature of the hot bath will be ...... $^{\circ}C$.

$A$ 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 $g$)?