One mole of an ideal gas is allowed to expand freely and adiabatically into vacuum until its volume has doubled. Which of the following statements is $NOT$ true concerning this expansion?

$9.0 \ g$ of $H_2O$ is vaporised at $100 \ ^oC$ and $1 \ atm$ pressure. If the latent heat of vaporisation of water is $x \ J/g$,then $\Delta S$ is given by

Arrange the following in order of magnitude of work done by the system / on the system at constant temperature:
$(a)$ $|w_{reversible}|$ for expansion in infinite stage.
$(b)$ $|w_{irreversible}|$ for expansion in single stage.
$(c)$ $|w_{reversible}|$ for compression in infinite stage.
$(d)$ $|w_{irreversible}|$ for compression in single stage.
Choose the correct answer from the options given below:

Assertion $(A)$: If heat of combustion of $C_2H_6$ is $X \ kJ \ mol^{-1}$,heat liberated on combustion of $150 \ g$ of $C_2H_6$ is $5X \ kJ$.
Reason $(R)$: Enthalpy is an extensive property.

Identify the correct statements from the following:
$I$. $\Delta_{r} G$ is zero for $A \rightleftharpoons B$ reaction.
$II$. The entropy of pure crystalline solids approaches zero as the temperature approaches absolute zero.
$III$. $\Delta U$ of a reaction can be determined using a bomb calorimeter.

$0.3 \ g$ of ethane undergoes combustion at $27^{\circ} C$ in a bomb calorimeter. The temperature of the calorimeter system (including the water) is found to rise by $0.5^{\circ} C$. The heat evolved during combustion of ethane at constant pressure is $....... kJ \ mol^{-1}$. (Nearest integer) [Given: The heat capacity of the calorimeter system is $20 \ kJ \ K^{-1}$,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$. Assume ideal gas behaviour. Atomic mass of $C$ and $H$ are $12$ and $1 \ g \ mol^{-1}$ respectively]