Specific Heat Capacity: Why Do Some Substances Take More Energy?

[SarcasticSully]

When two substances have the same temperature, the particles have the same average kinetic energy, right? So why is it that some substances take more energy to increase the temperature one degree even if the increase in average kinetic energy is the same? I'm referring to specific heat capacities here.

 

[Borek]

Specific heat capacity of an ideal gas doesn't depend on the molar mass of the gas - which is both a clear sign you are thinking in the right direction (yes, there are cases where all that matters is the average kinetic energy), and also a clear sign of what you miss (hint: how does real gas differ from the ideal one?).

 

[DrDu]

When two substances have the same temperature, the particles have the same average kinetic energy, right? .

No, absolutely not. This may be true for monoatomic ideal gasses, but even when you compare monoatomic and diatomic gasses, there are differences in kinetic energy. I.e. the diatomic molecules have also rotational kinetic energy. At latest, when considering solids and liquids, kinetic energy doesn't serve at all as a measure of temperature. A valid definition of temperature is the change of total energy with entropy at constant volume.

 

[epenguin]

This is quite important.

Early 19th century chemists found that molar specific heats did appear about the same for all atomic solids. This is called the Dulong-Petit law. They justified this to themselves by arguments as or even more vague than yours

And it was damned useful to them. Extrapolating it allowed to give atomic masses to elements. Note that the law doesn't need to be exactly true for this purpose, approximately true will serve as well.

Then there were other properties - the 'colligative' properties - osmotic pressure, freezing point depression etc. that could be used to estimate atomic and molecular masses too.

Now here I am not very sure of the history, but as far as I know they all started as purely empirical laws. They are known by names of discoverers like Raoult, van't Hoff etc. I think they just used them without much explaining them, and I guess they just thought the Dulong-Petit law had the same status. (I remember at school we were only given these empirical laws with no theoretical explanations and we just did the calculations with them without questioning, like the laws were just good luck that solved a problem that otherwise you could see no way to crack - and I guess the early chemists were the same). As far as I know the colligative properties were only rationalised by Gibbs by the 3/4 century, I just looked up, and he was clear that specific heat was not one of them or was anomalous. Anyway I am not sure that his (formal, mathematical, macroscopic at that stage) work seeped into chemistry very fast.

Rather later there was a full molecular kinetic explanation like what you sketch. But, in brief, after the initial usefulness the law and its explanation didn't work very well and even had failures so clamorous as to call for a whole new theory of dynamics! Successes using some quantum assumptions, first by Einstein, and I think others on gasses, had a major influence (the Jeans report) persuading scientists to take these assumptions seriously. If I am not mistaken more than the black body and photoelectricity by themselves. I would guess that this is because you can talk about specific heats in purely mechanical terms without getting into the already hard to understand electromagnetism.

As you see I am hazy on the exact history of this issue, I had been meaning to ask in the History section about histories, books, about how the ideas re colligative properties etc. evolved.

What I meant to say is you'll meet up with the questions you raise at least twice in your studies, once in questions of atomic and molecular weight determination, and again in basic quantum mechanics.

 

[epenguin]

PS. But black body and specific heats as well as Brownian motion are all part of the general theme of how energy equilibrates itself between the various 'modes of motion' available to it. It has been said that this was a main theme of Einstein's work and as major an achievement as anything else of his.