$\frac{1}{24.63}$ mole of an ideal mono-atomic gas undergoes a reversible process for which $PV^3 = C$,where $C$ $(L^2 \cdot atm)$ is a constant. The gas expands from an initial volume of $1 \ L$ and an initial temperature of $300 \ K$ to a final volume of $2 \ L$. The heat lost to the surroundings by the gas is ...... $J$.

Identify the incorrect statement among the following:

Which of the following graphs is incorrect?

Two gases $X$ (molecular weight $M_{X}$) and $Y$ (molecular weight $M_{Y}$; $M_{Y} > M_{X}$) are at the same temperature $T$ in two different containers. Their root mean square velocities are $C_{X}$ and $C_{Y}$ respectively. If the average kinetic energies per molecule of two gases $X$ and $Y$ are $E_{X}$ and $E_{Y}$ respectively, then which of the following relation$(s)$ is(are) true?

Two statements are given below.
Statement-$I$: The ratio of the molar volume of a gas to that of an ideal gas at constant temperature and pressure is called the compressibility factor.
Statement-$II$: The $RMS$ velocity of a gas is directly proportional to the square root of $T(K)$.
The correct answer is

At $100\,^\circ\text{C}$ and $1 \, \text{atm}$ pressure,if the density of liquid water is $1.0 \, \text{g cm}^{-3}$ and the density of water vapor is $0.0006 \, \text{g cm}^{-3}$,then the volume occupied by water molecules in $1 \, \text{L}$ of steam is ............. $\text{cm}^3$.