# I The second law of thermodynamics -- What does "from cold to hot" mean?

#### saar321412

in Clausius formulation, what does the phrase "from cold to hot" means?
I can understand it intuitively but in the language of the zero and first laws, we have not defined a temperature scale, only equivalence classes of systems that will be in equilibrium with each other (systems with the same value of the empirical we defined by a reference system).

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#### sysprog

It's clear enough, without going through the specifics, that 'from cold to hot' ordinarily means from a reservoir of lesser molecular motion to a reservoir of greater molecular motion. The Wikipedia Clausius Theorem article satisfactorily explains the specifics and the mathematics. The theorem is valid for the special case class of reversible processes.

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#### Andrew Mason

Homework Helper
in Clausius formulation, what does the phrase "from cold to hot" means?
I can understand it intuitively but in the language of the zero and first laws, we have not defined a temperature scale, only equivalence classes of systems that will be in equilibrium with each other (systems with the same value of the empirical we defined by a reference system).
Relative temperature is essentially a measure of the direction that heat flows between two bodies in thermal contact i.e. heat flow always occurs from higher to lower temperature. So unless temperature has some other definition, a law that says that heat cannot flow from cold to hot is merely a tautology.

You need kinetic theory to explain what temperature is. Clausius made very important contributions to the development the kinetic theory of gases. By analysing the physics of motion of the molecules of gases, if one gas (A) is put into physical contact with another gas (B) and the average translational kinetic energy of A's molecules is greater that of the molecules of B, the average translational kinetic energy of B's molecules will increase and that of A will decrease. Clausius showed that no matter how a system is configured, one cannot have a result in which the only change to the system and surroundings is an increase of the translational kinetic energy of the molecules of A and a decrease in that of B.

So, if temperature is defined as the average translational kinetic energy of the molecules of a body that is in thermodynamic equilibrium, it fits with the original concept of temperature. And that is essentially how termpature is defined (although for reasons having to do with quantum mechanics, that definition requires refinement at temperatures close to absolute zero).

AM

#### sophiecentaur

Gold Member
So unless temperature has some other definition, a law that says that heat cannot flow from cold to hot is merely a tautology.
Yes. "From Hot to Cold" means the direction that the Energy flows. The relationship is monotonic so it always flows the same way, whatever the temperatures or the numbers you have marked on the 'thermometer'.
I never wondered before why all the scales seem to have hot as a more positive number than cold. Is it really just arbitrary or is there something intuitive?

#### sysprog

I never wondered before why all the scales seem to have hot as a more positive number than cold. Is it really just arbitrary or is there something intuitive?
All non-zero absolute values are positive, and similarly, all motion, in any direction, can be regarded as positive compared to stillness. Although deceleration is negative compared to acceleration, and you could switch the signs, warmer than absolute zero would still mean more than zero molecular motion, so I think the positivity of temperatures, on an absolute scale, is neither just arbitrary nor merely intuitive, but based on empirically observable physical fact.

#### gmax137

wiki said:
From 1743, the Celsius scale is based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm pressure. Prior to 1743, the scale was also based on the boiling and melting points of water, but the values were reversed (i.e. the boiling point was at 0 degrees and the melting point was at 100 degrees). The 1743 scale reversal was proposed by Jean-Pierre Christin.
From:

https://en.wikipedia.org/wiki/Celsius

#### sophiecentaur

Gold Member
but based on empirically observable physical fact.
I think that is not an argument. You are justifying it post hoc, based on what we 'know' about the energy etc etc but thermometers were used before thermodynamics was understood.
However, @gmax137 (thank you) has quoted an example of a scale that's the other way round. This would particularly make sense for someone who was trying to refrigerate things because the colder the more difficult it becomes. Down in the 0K regions, it's particularly reasonable - like speeds just below c.

#### sysprog

sophicentaur said:
I think that is not an argument. You are justifying it post hoc, based on what we 'know' about the energy etc etc but thermometers were used before thermodynamics was understood.
The phrase 'slow as molasses in January' comes to mind. Speed has always been regarded as positive. That's true in any direction; for example, even when oarsmen row the boat in the direction opposite to that toward which they are facing, they still understand that the coxswain's more frequent stroke calls urge them to a positively greater speed. I think the recognition of the correlation of hotter to faster is ad hoc, not post hoc, and was commonly recognized long before any formalization of thermodynamics. Rubbing your hands together faster makes them hotter, running positively faster makes you positively warmer, and freezing something decreases its speed all the way to a stop.

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#### Anand Sivaram

I can understand it intuitively but in the language of the zero and first laws, we have not defined a temperature scale
We have the Kelvin scale as an absolute scale only. It depends upon 2 temperatures - Absolute Zero at 0K and Triple Point of Water at 273.16K. These temperatures are absolute means, they happen at a particular temperature and pressure and they could not vary. Where as both melting and boiling point of water could vary with pressure.
For convenience sake, 1K difference is kept as 1C difference.

"The second law of thermodynamics -- What does "from cold to hot" mean?"

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