# The Conceptual Side of Specific Heat Capacity

1. Feb 9, 2007

### Izzhov

I am a beginner in thermodynamics; all I know is how heat is transferred, rotational/translational/vibrational/internal energy, and the law of conservation of energy. I recently learned about specific heat capacity, and I was wondering: why is it that different substances convert varying ratios of the heat they receive into internal energy, and what happens to the rest of the energy. Also, what (physically) in a particle determines how much of its heat will be converted into internal energy? Finally, is there any substance that converts 100% of the heat it receives into internal energy?

2. Feb 9, 2007

### arunma

I'm no chemistry major, but I think I can partially answer this question. I believe that a compound's specific heat is governed by the nature of its molecular chemical bonds. This would imply, for example that the covalent bonds (O-H) in water molecules are capable of absorbing more energy without breaking than most other compounds (since water has a relatively high specific heat).

3. Feb 9, 2007

### Izzhov

But how does the fact that they have the ability to absorb more energy without the bonds breaking explain the fact that it requires more heat to raise the temperature? From what I gather, this question seems to be more one of efficiency (i.e. how much of the heat is converted into internal energy and how much is converted into rotational/etc).

4. Feb 9, 2007

### cesiumfrog

Is this just a degrees of freedom thing? If you put energy in a block of metal, all the atoms can really do is to vibrate. If you put the same amount of energy into the same mass of water, the molecules can move about, spin, stretch and wobble (plus, there's more particles there to begin with) so it takes more energy to get them to also vibrate the same amount as the metal.

Conceptually, consider the thermometer+material system. At thermal equilibrium, every degree of freedom (of every particle in this combined system) will have the same amount of energy on average. The height of the thermometer is obviously proportional to the average energy per degree of freedom (firstly of the mercury particles), so (at a given temperature) the total energy must be be determined by total number of particles and degrees of freedom in the material.

arunma, I don't think it has anything to do with breaking bonds. More that something like He gas (spherically symmetric) can't rotate (since, er, you wouldn't be able to detect if it did.. I think this is a QM thing) whereas H2 gas (little diatomic molecules) obviously can (although not about their axis of symmetry.. whereas steam molecules can, giving it an even higher capacity per mol).

5. Feb 10, 2007

### Gokul43201

Staff Emeritus
Actually, most substances have the same molar heat capacity (per accessible degree of freedom). You will see departures, when certain degrees of freedom are partially constrained, or in the case of metals at low temperatures, there will be departures due to the contribution to the internal energy from the free electrons. There are also some other more exotic deviations from the expected heat capacity behavior for some materials.

All ideal gases of the same atomicity (and hence having the same number of degrees of freedom) have, in theory, the same (molar) specific heat. The same is also true of all crystalline solids (at high enough temperatures - see Dulong-Petit law).

6. Feb 10, 2007

### Izzhov

Okay... I got think I most of that, but what are departures and degrees of freedom?