Internal energy change during phase change


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> 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.
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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 $\Delta V$?


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