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I found somewhere that in 1st order phase transition , at the transition temperature , specific heat of the system diverges. Can anyone explain me why and how ?

Tulika Tripathy
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  • Ya got it. But is it always the case ?? Like if we go the other way round . Like from water to ice ? Change in temp will always be zero for 1st order phase transition ? – Tulika Tripathy Jan 09 '17 at 07:30
  • Yes, there is no temperature change during phase transitions. http://chemistry.stackexchange.com/questions/15852/during-a-phase-change-in-matter-why-doesnt-the-temperature-change – Abhijeet Melkani Jan 09 '17 at 07:55
  • Keep in mind though that there are phase-transitions that are second order (water-steam system). And if those happen at the critical point there is no clear difference between the two states and there is no "discontinuity". I don't think you need to worry about that right now. – Abhijeet Melkani Jan 09 '17 at 07:59
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    The latent heat at the phase transition corresponds to a jump in the internal energy. And since the specific heat is related to the derivative of the internal energy, it diverges. See also http://physics.stackexchange.com/questions/80245/first-and-second-order-phase-transitions – SimonS Jan 09 '17 at 09:45
  • Are you familiar with the Dirac delta function from mathmatics? – Chet Miller Jan 09 '17 at 12:35
  • Yes.. somewhat I know.. – Tulika Tripathy Jan 10 '17 at 13:39

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Take the example of ice-water system in its melting point(equilibrium). If you add heat to the system the temperature will not rise(only some more of the ice will melt).

The specific heat is change in heat($\delta$Q) per unit change in temperature($ \delta$T) but $\delta$T is zero here so specific heat tends to infinity.

Abhijeet Melkani
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