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### Topic: Explanation of differences in heat capacities.  (Read 6334 times)

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#### GeLe5000

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##### Re: Explanation of differences in heat capacities.
« Reply #15 on: September 28, 2015, 09:57:53 AM »
Hello. The conclusion, I suppose. I hope that I haven't bothered you too much.
From your last posts I conclude that when reading the rest of my textbook, I'll have to try to understand mechanical statistics (degrees of freedom, 3/2 kTâ€¦) and the interplay of thermodynamics and kinetics.

I'd have liked to show you a graph that helps me visualize the fact that temperature is a measure of the concentration of thermic energy, but wasn't able to insert the image. On the same graph, two series of points : the ratios of specific heat capacities for couples of metals (Al, Cu, Au, Fe, Pb, Pt, Ag) and the product (ratio moles in 1 Kg) x (ratio moles in 1 ml). There are 21 couples. As you can see on the Table, except for Lead (the three highest points), there's a good correlation between the two series.

I : ratios of specific heat capacities
II : product (ratio moles in 1 Kg) x (ratio moles in 1 ml)

Couple   I       II
Au/Fe   0,28   0,2
Au/Ag   0,56   0,55
Pb/Ag   0,56   0,29
Pt/Ag   0,61   0,605
Cu/Fe   0,83   0,88
Au/Pt   0,93   0,91
Pb/Pt   0,93   0,47
Au/Pb   1   1,9
Cu/Ag   1,7   2,4
Al/Fe   1,9   1,47
Fe/Ag   2,04   2,7
Al/Cu   2,3   1,67
Cu/Pt   2,8   3,94
Cu/Au   3   4,37
Cu/Pb   3   8,34
Fe/Pt   3,35   4,4
Fe/Pb   3,6   9,4
Al/Ag   3,9   4
Al/Pt   6,4   6,6
Al/Au   6,9   7,29
Al/Pb   6,9   13,9

#### mjc123

• Chemist
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##### Re: Explanation of differences in heat capacities.
« Reply #16 on: September 28, 2015, 11:22:56 AM »
Temperature is a measure of the average thermal (kinetic) energy of the molecules, not the concentration of thermal energy (if by that you mean energy per unit volume). Consider a lump of gold at 300K in thermal equilibrium with gaseous helium at 300K. Or He at 300K and 0.1 atm in thermal equilibrium, via a partition, with He at 300K and 10 atm. The average kinetic energy of the atoms is the same (that's the definition of temperature), but the concentration obviously isn't.
If you look at the table in this article https://en.wikipedia.org/wiki/Heat_capacity you will see that for many metals, particularly transition metals, the volumetric heat capacity is roughly similar, at about 2-2.5 J/cm3/K. This is because their molar volumes are roughly similar, around 10 cm3/mol or so, and their molar heat capacities are all around 3R. In that case your plot reduces to a correlation between heat capacity ratio and inverse ratio of atomic weights, as we expect. Molar volumes tend to be higher for the s and p block metals, which is why lead doesn't fit the trend.