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Many books state that when there is no change in temperature $\Delta U$ is equal to zero. Why is this not applicable for phase transitions? I have had this question for a while now and have been unable to find an answer to it

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    $\begingroup$ "when there is no change in temperature ΔU is equal to zero." This is true of ideal gases, not general at all! $\endgroup$ – Buck Thorn Sep 21 at 8:02
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Such books forget to mention, or you may have not noticed such notes, that $\mathrm{d}T=0 \implies \mathrm{d}U=0$ does not apply to phase transitions because there is heat exchange at constant temperature, related to different energy of different phases at the same temperature.

E.g. by water boiling, water gains about 5.5 times more energy than by heating it from its freezing to boiling poit.

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