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Why does adding solutes to pure water lower the the specific heat?

Why do higher concentration salt solutions heat up more quickly?

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They don't. Although they do get hotter before they boil. Can you give a bit more info so we can see what the background to your question is. –  John Rennie Jun 21 '12 at 17:05
@JohnRennie: I thought this initially too, but the salt can reduce the specific heat of the water by preventing motion in a cage. –  Ron Maimon Jun 21 '12 at 17:06
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marked as duplicate by Ron Maimon, Qmechanic, David Z Sep 3 '12 at 18:34

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3 Answers

One spurious reason is that the salt suppresses evaporation, but this is not essential, and you would only see it in open containers.

The essntial reason is explained here: Why does adding solutes to pure water lower the the specific heat? . The salt becomes ions, and the ions hold a rigid cage of water molecules around them which are not allowed to vibrate individually. The reduction in the vibration degrees of freedom due to these cages reduces the specific heat by an amount roughly commensurate with the specific heat of the introduced salt, at most maybe 10 times bigger, since it's order-1 moelcules in the cage per salt atom.

The reason that you get freezing out near ions is that the water is a polar molecule, and charged ions have interactions with the water molecules on the atomic scales that is two orders of magnitude bigger than kT. This allows the cage to form and to stay rigid enough that its oscillations are quantum mechanically frozen out. Without quantum mechanics, any spring, no matter how rigid, contributes almost the same amount to the specific heat, since classical systems have equipartition which doesn't allow the specific heat to go below .5 kT per degree of freedom (the kinetic energy), which is usually one kT per degree of freedom (harmonic spring), and which is not sensitive to the stiffness of the spring, only to the shape of the potential.

The strength of the polar-molecule ion interaction is estimated in this answer: Please explain the physics of a Cloud Chamber

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Having claimed that solutes don't affect the specific heat not only do I have to admit I'm wrong, but I've found a paper explaining the effect by no less a person than Fritz Zwicky, better known to many of us as a cosmologist.

Anyhow, the paper is at http://authors.library.caltech.edu/8821/1/ZWIpnas26a.pdf

Zwicky finds that the biggest effect is, to use his words: the water molecules act as rigid electric dipoles, and a dipole in the inhomogenous field of an ion will be attracted to it. The result of this attraction is a high pressure around the ion, and because the specific heat of water is strongly changed by pressure this effect has a big effect on the specific heat.

There are several other possible contributions, but Zwicky shows these are small compared to the pressure effect.

The paper is beautifully written and I strongly recommend having a look at it.

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+1 and nice find! –  Ron Maimon Jun 22 '12 at 7:31
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Adding salt in water will definitely lower the specific heat capacity of the solution but it will also increase the boiling point of the solution. i.e. Salt water would DEFINITELY get to 100° more quickly, but would it would reach 102° C or 103° C or whatever temperature before it boils.
The boiling point of a liquid (a solvent) will be higher when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-volatile solute, such as a salt, is added to a pure solvent, such as water.
EDIT : Added Explaination:
The boiling point elevation is a colligative property, which means that it is dependent on the presence of dissolved particles and their number, but not their identity. It is an effect of the dilution of the solvent in the presence of a solute. It is a phenomenon that happens for all solutes in all solutions, even in ideal solutions, and does not depend on any specific solute-solvent interactions. The boiling point elevation happens both when the solute is an electrolyte, such as various salts, and a nonelectrolyte. In thermodynamic terms, the origin of the boiling point elevation is entropic and can be explained in terms of the vapor pressure or chemical potential of the solvent. In both cases, the explanation depends on the fact that many solutes are only present in the liquid phase and do not enter into the gas phase (except at extremely high temperatures).

Put in vapor pressure terms, a liquid boils at the temperature when its vapor pressure equals the surrounding pressure. For the solvent, the presence of the solute decreases its vapor pressure by dilution. A non-volatile solute has a vapor pressure of zero, so the vapor pressure of the solution is less than the vapor pressure of the solvent. Thus, a higher temperature is needed for the vapor pressure to reach the surrounding pressure, and the boiling point is elevated.

Put in chemical potential terms, at the boiling point, the liquid phase and the gas (or vapor) phase have the same chemical potential (or vapor pressure) meaning that they are energetically equivalent. The chemical potential is dependent on the temperature, and at other temperatures either the liquid or the gas phase has a lower chemical potential and is more energetically favorable than the other phase. This means that when a non-volatile solute is added, the chemical potential of the solvent in the liquid phase is decreased by dilution, but the chemical potential of the solvent in the gas phase is not affected. This means in turn that the equilibrium between the liquid and gas phase is established at another temperature for a solution than a pure liquid, i.e., the boiling point is elevated.

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This is false, as seems to be experimentally clear, see the linked question. –  Ron Maimon Jun 21 '12 at 17:13
@RonMaimon I have added explaination. And the experiment which you are talking about is different than what is asked here. –  Luftwaffe Jun 21 '12 at 17:51
Ok, I see you just edited out the false statements--- that's good. But the issue of boiling point elevation is a total red herring. The question is about the specific heat reduction, which is classically impossible and very counter-intuitive. Adding degrees of freedom intuitively raises the specific heat. –  Ron Maimon Jun 21 '12 at 18:12
@RonMaimon I have clearly stated in my answer's first line "Adding salt in water will definitely lower the specific heat capacity of the solution but it will also increase the boiling point of the solution. i.e. Salt water would DEFINITELY get to 100° more quickly, but would it would reach 102° C or 103° C or whatever temperature before it boils." It now on the person who has asked the question what does he mean by "quicker' - is it the time taken to heat up or the temperature to reach before it boils. –  Luftwaffe Jun 21 '12 at 18:14
Since when does "quickly" mean "hotter"? You edited out your totally false original opening statements and replaced them with correct statements. You say it DEFINITELY would get to 100 more quickly (and therefore get more quickly to 102, since going from 20-100 or 20-102 is no difference at all), but this is the whole question--- why is this? You don't explain why putting salt in lowers the specific heat, it's a really strange thing, and it means ionic water solutions are crazy. –  Ron Maimon Jun 22 '12 at 0:46
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