# Specific Heat Capacity & Temperature

by Christopher M
Tags: specific heat, temperature, thermodynamics
 P: 3 This is not a homework question, just a question about physics that seems too basic to post in the main physics discussion forum. Please let me know if it is misplaced. Temperature is average molecular kinetic energy. Is it therefore correct to say that a material's specific heat capacity depends entirely on the following question: when you put energy into the material, how does it divide that energy up between, on the one hand, kinetic energy of molecules, and on the other hand, other forms of energy? In other words, is the reason that different substances have different specific heat capacities simply that some substances, when they take in energy, store it in forms other than molecular kinetic energy? Thanks.
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P: 26,148
 Quote by Christopher M Temperature is average molecular kinetic energy. Is it therefore correct to say that a material's specific heat capacity depends entirely on the following question: when you put energy into the material, how does it divide that energy up between, on the one hand, kinetic energy of molecules, and on the other hand, other forms of energy? In other words, is the reason that different substances have different specific heat capacities simply that some substances, when they take in energy, store it in forms other than molecular kinetic energy?
Hi Christopher! Welcome to PF!

If we're talking about a solid, I've always assumed that the different specific heat capacities are because the molecules vibrate back and forth differently because they're more or less strongly bound.

I don't see what other forms (than kinetic energy) the energy could go into.
 P: 3 Thanks for the response! But if energy goes into making the molecules vibrate back and forth more energetically, doesn't that increase temperature (since temperature is average kinetic energy)? In other words, if all the energy goes into kinetic energy -- and temperature is average kinetic energy -- how could the same amount of energy cause the temperature of different materials to rise by different amounts?
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Specific Heat Capacity & Temperature

 Quote by Christopher M Thanks for the response! But if energy goes into making the molecules vibrate back and forth more energetically, doesn't that increase temperature (since temperature is average kinetic energy)? In other words, if all the energy goes into kinetic energy -- and temperature is average kinetic energy -- how could the same amount of energy cause the temperature of different materials to rise by different amounts?
Hi Christopher!

Because only the translational vibrations determine the temperature (vie the Boltzmann equation), but a lot of the energy goes into rotational and other internal modes. For more detail, see wikipedia:

3.3 The internal motions of molecules and specific heat

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