Internal energy change during phase change Ice at $\mathrm{0\ ^\circ C}$ is converted to water at $\mathrm{0\ ^\circ C}$. If $\Delta H$ for the transition of ice to water is $\mathrm{1440~cal}$, calculate the change in internal energy.


Since internal energy $\Delta U=nC_V\Delta T$ and $\Delta T=0$, shouldn't $\Delta U=0$?

But if I use $ 
\Delta H=\Delta U +\Delta nRT$, I get $\Delta U=\Delta H\neq 0$.
You are considering the $\Delta H$ and the $\Delta U$ between the following two thermodynamic equilibrium states:

State 1:  1 mole of ice at 0 C and 1 atm.

State 2:  1 mole of liquid water at 0 C and 1 atm.

The relationship between $\Delta H$ and $\Delta U$ at constant pressure is:
$$\Delta H=\Delta U + p\Delta V$$where V is molar volume.  What is the molar volume of ice?  What is the molar volume of liquid water?  What is $\Delta V$?