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It is my understanding that entropy and heat capacity essentially measure the same thing. Since entropy is the ratio of heat (translational, rotational, vibrational movement) to temperature (translational movement), a substance with higher entropy (heat/temperature ratio) would require more heat to raise a certain temperature, which is the definition of heat capacity. Why then, is the heat capacity of liquid water around 4.2 J/g-K while for water vapor, it's only 2.0 J/g-K when vapor has more entropy?

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  • $\begingroup$ It would be perhaps clearer to state that the heat capacity is directly related to the second derivative of the free energy. Since the free energy has both an enthalpic and entropic contribution, the rest is left as an exercise... $\endgroup$ – Jon Custer Mar 13 '16 at 15:47
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    $\begingroup$ Well, you see that entropy and heat capacity are not always directly related. That being said, water is quite unusual in this respect. $\endgroup$ – Ivan Neretin Mar 13 '16 at 16:34

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