$A$ partition divides a container having insulated walls into two compartments $I$ and $II$. The same gas fills the two compartments. Based on the values given in the figure,the ratio of the number of molecules in compartments $I$ and $II$ is

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$, the piston moves through a length of $5 \, cm$. The length of the cylindrical vessel in $cm$ is:

At $N.T.P.$,$1 \text{ cm}^3$ of oxygen and $1 \text{ cm}^3$ of hydrogen are kept in different containers. Which will have a greater number of molecules?

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

When the temperature of a gas at constant volume is increased by $5^{\circ}C$,its pressure increases by $0.5\%$ of its initial value. The initial temperature of the gas is..... $K$.

Two different isotherms representing the relationship between pressure $p$ and volume $V$ at a given temperature for the same ideal gas are shown for masses $m_1$ and $m_2$ of the gas respectively in the figure given. Then: