When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ} C$,its pressure increases by $0.4 \%$. The initial temperature of the gas is ..........$K$.

Hydrogen gas is filled in a balloon at $20^\circ C$. If the temperature is increased to $40^\circ C$ while the pressure remains constant,what fraction of the original Hydrogen gas will escape from the balloon?

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 $2V_0$.

An insulated cylinder of volume $60\,cm^{3}$ is filled with a gas at $27^{\circ}C$ and $2$ atmospheric pressure. Then the gas is compressed making the final volume $20\,cm^{3}$ while allowing the temperature to rise to $77^{\circ}C$. The final pressure is . . . . . . atmospheric pressure.

$A$ 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 $g$)?

What is an ideal gas? Write the state equation for an ideal gas. Write and explain the different laws relating to gases.