$X$ is an extensive property and $x$ is an intensive property of a thermodynamic system. Which of the following statement$(s)$ is (are) correct?

When $1 \ mol$ of a gas is allowed to expand freely in a vacuum,what is the work done during the process in Joules?

The work done during reversible isothermal expansion of one mole of hydrogen gas at $25^{\circ}C$ from a pressure of $20 \ atm$ to $10 \ atm$ is
(Given $R = 2.0 \ cal \ K^{-1} \ mol^{-1}$)

Given below are two statements $ : $
Statement $I :$ When a system containing ice in equilibrium with water $(\text{liquid})$ is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted.
Statement $II :$ At the melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice, and the kinetic energy of molecules is not increased at the melting point.
In the light of the above statements, choose the correct answer from the options given below $ : $

For the reaction of nitrogen with hydrogen to form ammonia,$\Delta H^o = -92.2 \ kJ/mol$. If the reaction is carried out at a constant pressure of $20.0 \ atm$ and a volume change of $-1.16 \ L$,calculate the change in internal energy $(\Delta U)$ in $kJ$.

Which of the following is not a state function?
$(I) \, q + W \, (II) \, q \, (III) \, W \, (IV) \, H - TS$