# 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 $\Delta U=\Delta H\neq 0$.

• The equation you wrote for $\Delta H$ applies only to an ideal gas (assuming that the nRT is all in parenthesis). What is the general equation for $\Delta H$, since we are dealing here with a liquid and a solid? – Chet Miller Jan 16 '16 at 15:01
• Does the equation you wrote for $\Delta U$ when there is a change of phase? – Chet Miller Jan 16 '16 at 15:36
• @ChesterMiller I don't understand you. – Aditya Dev Jan 16 '16 at 15:55
• I meant to say, does the equation you wrote apply... – Chet Miller Jan 16 '16 at 16:09
• @ChesterMiller so $\Delta U =nC_v\Delta T$ is only for expansion/contraction of gases? – Aditya Dev Jan 16 '16 at 22:19

You are considering the $\Delta H$ and the $\Delta U$ between the following two thermodynamic equilibrium states:
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 $\Delta V$?