Which amongst the following options is the correct relation between change in enthalpy and change in internal energy?

An ideal gas undergoes a cyclic transformation starting from the point $A$ and coming back to the same point by tracing the path $A$ $\rightarrow B$ $\rightarrow C$ $\rightarrow D$ $\rightarrow A$ as shown in the three cases above. Choose the correct option regarding $\Delta U$.

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 $ : $

Which of the following is not true?

Which of the following sets represents the normal physical states of the elements concerned at $25\,^{\circ}C$ and $1 \ bar$ pressure,for which $\Delta H^{\circ}_{f} = 0$?

$A$ perfect gas $(0.1 \ mol)$ having $\overline{C}_{v}=1.50 \ R$ (independent of temperature) undergoes the transformation shown in the graph from point $1$ to point $4$. If each step is reversible,the total work done $(w)$ while going from point $1$ to point $4$ is $(-)$ . . . . . . $J$ (nearest integer). [Given: $R=0.082 \ L \ atm \ K^{-1} \ mol^{-1}$,$1 \ L \ atm = 101.3 \ J$]