$A$ gas is filled in a cylinder. If its temperature is increased by $20\%$ and its volume decreases by $10\%$, what percentage of the gas will have leaked out?

An ideal gas initially at pressure $1 \, bar$ is being compressed from $30 \, m^{3}$ to $10 \, m^{3}$ volume and its temperature decreases from $320 \, K$ to $280 \, K$. Find the final pressure of the gas (in $bar$).

$A$ graph between volume $V$ and absolute temperature $T$ is obtained when a given mass of a gas is heated. During the heating process from state-$1$ to state-$2$,the pressure

By using the ideal gas equation $PV = \mu RT$,write the value,unit,and dimension of $R$.

$A$ vessel with an open mouth contains air at $60^{\circ}C$. When the vessel is heated up to temperature $T$,one-fourth of the air goes out. The value of $T$ is ..... $^{\circ}C$

Three containers of the same volume contain three different gases. The masses of the molecules are $m_1, m_2$ and $m_3$ and the number of molecules in their respective containers are $N_1, N_2$ and $N_3$. The gas pressures in the containers are $P_1, P_2$ and $P_3$ respectively. All the gases are now mixed and put in one of the containers. The pressure $P$ of the mixture will be