What is Heat

1. Jun 7, 2013

StarsRuler

¿ What is heat, really, is the energy that in summatory of energies can´be written in function of temperature? It appears in primitive formulations of first principle of thermodynamics, but I don´t understand exactly its meaning

2. Jun 7, 2013

Staff: Mentor

There is a great Heat entry in the PF Library, but the Library appears broken at the moment. The Mentors and Admins are working on it...

3. Jun 7, 2013

DrDu

Heat is that part of change of internal energy of a thermodynamic system which is not due to classical work, i.e. mechanical or electrical or work done by electromagnetic fields.

4. Jun 8, 2013

lightarrow

Heat is the energy exchanged between two systems in contact, caused by a temperature difference only.
Note that it's incorrect to say "exchange of heat", even if many text write it.

5. Jun 8, 2013

Andrew Mason

"Heat" can be used in the colloquial sense to mean "thermal energy", which is the internal energy of a body due to its temperature (ie. the translational kinetic energies of molecules that follow the characteristic Maxwell-Boltzmann distribution).

But in thermodynamics, heat is used to mean Q (e.g. the first law: Q = ΔU + W) which is the flow of energy from one body to another due to a difference in temperature, as distinct from the energy flow due to mechanical work. This is how the concept of "heat" originated because it was thought that "heat" was a substance that flowed through bodies.

To avoid confusion between the colloquial use and the scientific use, Q is often referred to has "heat flow" rather than just "heat". This makes it clear that Q is not something that can exist in a body. Rather, it is an exchange of energy between bodies.

AM

6. Jun 8, 2013

Heat is the measure of the average kinetic and potential energy of the molecules or atoms of a body.Heat is a type of energy-meaning it can be transformed from on form to another.Heat flows only from a higher temperature to a lower temperature.

7. Jun 8, 2013

Andrew Mason

None of this is really correct:

1. Heat is the measure of the average kinetic and potential energy of the molecules or atoms of a body.

Internal energy (U), not heat (Q), is the measure of the average kinetic and potential energy of the molecules of a body in thermal equilibrium. (note: Temperature is the measure of the average translational kinetic energy of the molecules of a body in thermal equilibrium).

2. Heat is a type of energy-meaning it can be transformed from one form to another.

Heat (Q), or heat flow, represents a transfer of energy from one body to another. It is not correct to say that Heat is energy. Heat could be viewed as the work done at the molecular level by the molecules in one body on the molecules of another body.

Since heat is an energy transfer (molecular work) and not energy (energy being the ability to do work), heat cannot be converted into other forms of energy. Rather, internal energy of a body (eg. a thermal reservoir) can be converted into mechanical energy via heat (eg. heat flow that occurs in a heat engine).

3. Heat flows only from a higher temperature to a lower temperature.

This would be true if you were to add the word "spontaneously". As stated, it says that a refrigerator is not possible. Of course, refrigerators cause heat flow from cold to hotter bodies to occur by supplying mechanical work.

AM

Last edited: Jun 8, 2013
8. Jun 8, 2013

lightarrow

I contest even the phrase "heat flow". If heat flows, what this flux is made of? Heat is just a transfer of energy (in peculiar conditions) so what "flows" is simply energy, not heat.

9. Jun 8, 2013

Andrew Mason

The concept of "energy flow" or "energy transfer" is just mental bookkeeping. Energy is just a number. But since energy is always conserved we can think of energy moving around.

I agree that heat (Q), like work (W), is not something that a body possesses and it is not conserved. So it is not something that "flows" mathematically or physically. It is a particular kind of energy transfer process that occurs in a thermodynamic process. We could call it "a transfer of energy by means other than mechanical work", but heat or heat flow is the conventional term.

We often use terms in science that are well understood but not really correct, like "electromotive force". Although they are not really correct, they help us model the phenomena in our minds and have gained acceptance by usage.

AM

10. Jun 9, 2013

tolove

Hey Andrew, could you check my understanding of heat? Is anything wrong with the following statement:

The internal energy (U) of an object (object being ideal single atom particles in either a gas, liquid, or solid state) is also referred to as the object's temperature (T) or translational kinetic energy (K).

If a relatively hot and cold substance are placed side by side (with a divider in the case of liquids and gasses to prevent convection, and neglecting radiation), the comparatively faster moving particles of the hot substance repeatedly slam into the slower particles belonging to the colder object. During this process, the temperature of the colder object rises, while the temperature falls in the hotter object. This process is described as a flow of heat (Q), even though no physical thing moves from one object to the other.

"Heat is the transfer of molecular work and not the ability to perform work."

I'm not sure I understand this quote.. could you elaborate on this? Heat (Q) is not conserved? If heat (Q) is defined in terms of changes in internal energy (U), and internal energy (U) is conserved, isn't heat flow (Q) also conserved?

Thank you very much for your time!

11. Jun 9, 2013

Andrew Mason

There is an important difference between internal energy and temperature. Temperature is a measure of one aspect of internal energy: the energy due to the motion of the centres of mass of the molecules that comprise the body. These molecules can have kinetic energy due to other kinds of motion - vibration and rotation about different axes - that do not involve the motion of the centres of mass of the molecules. These kinds of motion do not contribute to the body's temperature. Also, molecules can have potential energy due to inter-molecular forces. This potential energy is part of the internal energy but does not contribute to temperature.

You have the right idea. But it is important to keep in mind that the speed distribution of molecules follows Maxwell-Boltzmann statistics: the molecules in the hotter body are not all moving faster than those in the cooler one but, statistically, the collisions result in the average kinetic energy of the molecules in the cooler body increasing and the average KE of the molecules in the hotter body decreasing. If it continues long enough, the two bodies reach thermal equilibrium and have the same temperature.

Where did you get the quote? I said that heat could be viewed as the work done at the molecular level by the molecules in one body on the molecules of another body.

Work is something that a body does by applying a force through a distance. That work results in an "transfer" of energy ie a transfer of "the ability of a body to do work" to another body.

For example: A fast molecule colliding with a slow molecule. The fast molecule does work on the slow molecule, thereby increasing the slower molecule's kinetic energy. The slower molecule does negative work on the faster molecule (by applying an equal but opposite force through the same distance), thereby reducing the kinetic energy of the faster one. Since the increase in energy of the slow one is equal to the decrease in energy of the faster one, we can think of this as a "transfer of energy".

Internal energy of a system is not conserved. It can change. It can change because energy can flow into our out of the system. It can flow into our out of the system because of heat flow into (Q), or out of (-Q), or work being done by (W), or on (-W), the system .

Heat and work represent transfers of energy into or out of the system. ΔU represents a change in energy of the system. The first law just says that the sum of all the transfers of energy into and out of the system must equal the change in energy of the system: ΔU = Q - W. Q, W and U can all change. But ΔU = Q - W is always true once everything settles down.

AM

Last edited: Jun 9, 2013
12. Jun 9, 2013

tolove

Could you see if I understood you correctly?

1) When neglecting subatomic properties, vibration, and rotation temperature (eg translational kinetic energy) is an exact measure of the internal energy of an 'ideal' substance.
2) Heat is an action. A substance cannot have heat (Q), rather, the substance has a temperature (T), which is a component of it's internal energy. When a temperature difference occurs, the substance performs a heat flow.
3) The internal energy of an isolated system is conserved. Components of the internal energy are not conserved, and may change form.

And an extra question on the subject: two perfectly insulated reservoirs of gas at equal temperatures are connected. In a modern view, is there a probability for a temperature difference to spontaneously occur between the two reservoirs?

Thank you very much again!!

13. Jun 9, 2013

Andrew Mason

You can say, for example, that for an ideal monatomic gas, temperature is proportional to the internal energy of the gas. That is because there are no inter-atomic forces and no rotational or vibrational modes in an ideal gas.

Temperature is not a component of internal energy. It is a measure of one component of internal energy: translational KE.

Whether a temperature difference between two bodies leads to heat flow depends on the connection between them.
If the system is isolated, it cannot exchange energy (or mass) with its surroundings. So Q = 0 and W = 0. So what does the first law tell you about U (internal energy)?

What change in the components of internal energy would change? You will have to describe the system. If the system is a gas in an equilibrium state, then the "components" of the internal energy (rotational, translational, vibrational kinetic energy and potential energy) should not change. If the system was a weight, rope and pulley, and a piston in a cylinder filled with gas, the components of the system's energy may well change.

You have to be careful in describing the reservoirs and the way they are connected. Are they at the same pressure? Is the volume fixed? Are they the same gas chemically? Does the connection allow the gases to mix?

AM

Last edited: Jun 9, 2013
14. Jun 9, 2013

tolove

Alright, I'm getting closer!

on 2), Translational KE is a component of internal energy; temperature is a measure of that motion.

on 3) For an isolated system, would it be better to say that internal energy remains constant rather than conserved? Those two words are very similar in meaning for me.

And the last part, I'm referring to the second law. In a classical sense, heat always spontaneously transfers from high to low temperature. However, in a modern view, is it correct to say that heat can spontaneously transfer from a low to a high temperature, just with an infinitesimally small chance of occurrence?

15. Jun 9, 2013

Andrew Mason

ΔU=0
Even in a classical sense there is always a non-zero probability that a system will spontaneously move to a state of non-equilibrium. That is because the second law is a statistical law.

The second law would say that the probability of observing a measureable net transfer of energy from the cold to the hot for a measureable time interval is so small that it will never happen anywhere in a gazillion lifetimes of the universe. So we call it a law.

AM

16. Jun 9, 2013

Rap

Temperature is related to translational kinetic energy EXCEPT at extremely low temperatures, so its incorrect to state flatly that temperature is a measure of the average translational energy.

Temperature is simply related to the energy per degree of freedom when that degree of freedom is classical, i.e. the energy levels that are significantly populated are so close together that the distribution of energy is essentially over a continuum and the distribution is Boltzmann. Such a degree of freedom is termed "unfrozen". When quantum effects start to appear (energy level spacing not negligible with respect to average energy), then the degree of freedom is partially or completely frozen.

At room temperature, translational degrees of freedom are unfrozen, maybe some others (rotation, vibration, etc) are too, maybe not. Kinetic temperature equals thermodynamic temperature. As you lower the temperature, other degrees of freedom start to freeze. The last degrees of freedom to freeze are the translational degrees of freedom. When that happens, kinetic temperature diverges from thermodynamic temperature. This occurs at EXTREMELY low temperatures (e.g Bose Einstein condensation and non-Boltzmann distributions). Unless you are working in these regimes, kinetic temperature is a good proxy for thermodynamic temperature, but statements like "internal degrees of freedom do not contribute to temperature" are deeply misleading. Translational degrees of freedom are just like any other degree of freedom, except that they are the last to freeze as the temperature drops.

17. Jun 10, 2013

Andrew Mason

That is the classical definition of temperature. See: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html

What is the definition of extremely low temperatures? At extremely low temperatures, the temperature of molecules is determined by directly measuring the translational speed of the molecules. That is how they measure temperatures in nano-Kelvins.

How are you suggesting temperature should be defined?

But in cases where the other degrees of freedom are active, the temperature is still determined the average translational kinetic energy of the molecules.

The problem with defining temperature as the average energy per degree of freedom is that it assumes that the equipartition theorem always applies. And, of course, it does not apply in many situations - not just at low temperatures.

Internal degrees of freedom contribute to heat capacity. So they certainly will affect the temperature of a body experiencing heat transfer. But the measure of that body's temperature is still determined by the average translational kinetic energy of the molecules.

Can you give us an example of any substance in which the translational degrees of freedom are frozen at some temperature?

AM

Last edited: Jun 10, 2013
18. Jun 10, 2013

Rap

Thermodynamic temperature is defined in the second law of thermodynamics, usually using a Carnot cycle. It makes no reference to particles or statistical mechanics. The second law says that the heat transferred $\delta Q$ can be expressed as $T\,dS$ where the thermodynamic temperature T is an intensive state function and entropy S is an extensive state function. It leaves the scales hanging, pick your own, Kelvin, Rankine, whatever.

No, in this case, you can just as well say the temperature is determined by any, some or all of the internal degrees of freedom (DOFs). Suppose you have five internal degrees of freedom, 3 translational, 2 rotational. As long as all those DOFs are unfrozen and sharing energy, you can just as well say that temperature is determined by the average total energy of the molecules, E=(5/2)kT, or by the translational DOFs: E=(3/2)kT, or by the internal DOFs: E=(2/2)kT or by any single DOF: E=(1/2)kT. Why not say that the x-component of the speed determines the temperature? You could, because all three translational DOFs are unfrozen and sharing energy, so it wouldn't matter if you did. You get the same answer no matter which degree(s) of freedom you choose.

Whenever it does not apply to a particular DOF, that DOF is partially or (practically) completely frozen. Every DOF has a temperature below which it must be described quantum mechanically, and the equipartition theorem becomes invalid. It begins to freeze. Below that temperature is "low temperature" for that DOF. Low temperatures for rotational DOFs in common gases may be room temperature. For translational DOF's "low temperature" is down in the nanokelvin range. That's what makes translational DOFs special - they are the last to freeze, but freeze they will.

A gas of bosons in a box, in which almost all the particles are at the ground energy level, only a small percentage in the first translational excited state, even less in the higher excited states. In other words, a Bose-Einstein condensate. Translational DOF's are nearly completely frozen. (No DOF is ever completely frozen except at unattainable absolute zero)

19. Jun 10, 2013

Andrew Mason

Do you really want to use a definition of temperature that pre-dates kinetic theory?

IF the equipartition theorem actually applied perfectly, of course you could say that the temperature is a measure of the kinetic energy associated with any of the active degrees of freedom - because they are all equal. But the problem is that it often does not apply. So what then do you use to determine the temperature? Answer: the translational kinetic energy. There is good reason for this: it is the difference in the translational KE between two bodies that causes spontaneous heat flow.

And how do they measure/define the temperature of a Bose-Einstein condensate?

AM

20. Jun 10, 2013

atyy

That article seems to support Rap's second law based definition, since it claims to define "kinetic temperature", not "temperature".

The same site has a discussion http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper2.html#c2 , and says at http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper2.html#c1 "Temperature is expressed as the inverse of the rate of change of entropy with internal energy, with volume V and number of particles N held constant. This is certainly not as intuitive as molecular kinetic energy, but in thermodynamic applications it is more reliable and more general."