$A$ jar contains a gas and a few drops of water at $T \, K.$ The pressure in the jar is $830 \, mm$ of mercury. The temperature of the jar is reduced by $1\%.$ The saturated vapour pressure of water at the two temperatures are $30 \, mm$ and $25 \, mm$ of mercury. Then the new pressure in the jar will be ..... $mm$ of $Hg$.

One kg of a diatomic gas is at a pressure of $8 \times 10^4 \; N/m^2$. The density of the gas is $4 \; kg/m^3$. What is the energy (in $\times 10^4 \; J$) of the gas due to its thermal motion?

The internal energy of $10 \, g$ of nitrogen at $S.T.P.$ is about ......... $J$.

Which one of the following schematic graphs best represents the variation of $p V$ (in Joules) versus $T$ (in Kelvin) of one mole of an ideal gas? (The dotted line represents $p V=T$)

An oxygen cylinder of volume $30 \ L$ has $18.20 \ \text{moles}$ of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to $11 \ \text{atm}$ at a temperature of $27^{\circ} \text{C}$. The mass of the oxygen withdrawn from the cylinder is nearly equal to (Given: $R = \frac{100}{12} \ \text{J mol}^{-1} \text{K}^{-1}$, molecular mass of $O_2 = 32 \ \text{g/mol}$, $1 \ \text{atm} = 1.01 \times 10^5 \ \text{Pa}$) (in $\text{kg}$)

$A$ very tall vertical cylinder is filled with a gas of molar mass $M$ under isothermal conditions at temperature $T$. The density and pressure of the gas at the base of the container are $\rho_0$ and $p_0$,respectively. Choose the correct statement$(s)$ if gravity is assumed to be constant throughout the container.