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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.

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

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    $\begingroup$ 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? $\endgroup$
    – Chet Miller
    Commented Jan 16, 2016 at 15:01
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    $\begingroup$ Does the equation you wrote for $\Delta U$ when there is a change of phase? $\endgroup$
    – Chet Miller
    Commented Jan 16, 2016 at 15:36
  • $\begingroup$ @ChesterMiller I don't understand you. $\endgroup$
    – Aditya Dev
    Commented Jan 16, 2016 at 15:55
  • $\begingroup$ I meant to say, does the equation you wrote apply... $\endgroup$
    – Chet Miller
    Commented Jan 16, 2016 at 16:09
  • $\begingroup$ @ChesterMiller so $\Delta U =nC_v\Delta T$ is only for expansion/contraction of gases? $\endgroup$
    – Aditya Dev
    Commented Jan 16, 2016 at 22:19

1 Answer 1

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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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  • $\begingroup$ So ∆H and∆U will denote the heat change and internal energy change between two equilibrium states at constant pressure? $\endgroup$
    – Scáthach
    Commented Feb 14, 2019 at 17:21
  • $\begingroup$ what is the equation to be applied for phase change? $\endgroup$
    – Khushi Ladha
    Commented Aug 9, 2020 at 3:07
  • $\begingroup$ @the.eleventh.letter I have no idea what you are asking. Please elaborate. $\endgroup$
    – Chet Miller
    Commented Aug 9, 2020 at 3:24
  • $\begingroup$ The question asked here was how to find ∆u when ∆h is given. However you ended up ur answer with questions 'what is molar volume of ice, water?' so I didn't quite understand that. $\endgroup$
    – Khushi Ladha
    Commented Aug 9, 2020 at 15:00
  • $\begingroup$ Did u mean, we jave to subtract molar volume of ice and water.. to find ∆v? $\endgroup$
    – Khushi Ladha
    Commented Aug 9, 2020 at 15:01

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