[Bored chemist]

"The potential energy of a strained lattice may be enormous"
yes, it was the cause of the Windscale fire- it made the graphite very hot...

No, it was the release of Wigner potential energy that raised the temperature. Problem is that once you reach the annealing temperature you can initiate a chain reaction that outstrips the cooling capacity of the system - as happened at Windscale.

So, what happened was the transfer from one particular degree of freedom to all the others.

As I said...
Quote from: Bored chemist on Yesterday at 08:57:08
However, when a body has a well defined temperature the energy per degree of freedom will be the same anyway.

[Bored chemist]

I think that the experimental  plot above plays important role in the development of equipartition theory, also the concept of degree of freedom. But the difference in the gradient of the curve shows that at least at some points, the energy distribution among different degrees of freedoms are not equal.

Or it shows that the number of degrees of freedom isn't an integer.

When heat capacity is 3R/2, we interpret this as the heat energy is distributed to translational motion equally in 3 spatial axes.
When heat capacity is 5R/2, the gas  has 2 additional degrees of freedom, which is thought to come from rotation in 2 axes. Each unit of additional heat energy will be distributed evenly over 5 available degrees of freedom, which are 3 translational and 2 rotational motion.
There's a point in the graphic where heat capacity is 4R/2. How should it be interpreted? Will additional heat energy be distributed evenly over 4 available degrees of freedom?

It depends.

[hamdani yusuf (OP)]

It depends.

On what, exactly?

[Bored chemist]

It depends.

On what, exactly?

Guess.
or, even better, learn science.

[Spring Theory]

Kelvin = Energy

It seems to imply that objects with the same temperature have the same energy, which is demonstrably false. 

It depends on the experimental set up and what objects you are talking about and the heat bath and equilibrium state, etc. I will have to think about that based on the photon concept.

My point was that Entropy is the log of something.  The log of something has no units.  To get to temperature, the Boltzmann constant simply converts energy into units of temperature. Kind of like you can convert Joules in units of kg m/s by multiplying it by 1.

The goal was to define what temperature (Kelvin) is.  It is in natural units of energy (which is generally accepted in the physics community):



Where E is the energy of the system and S is the Entropy as defined previously.

[alancalverd]

No, it was the release of Wigner potential energy that raised the temperature. Problem is that once you reach the annealing temperature you can initiate a chain reaction that outstrips the cooling capacity of the system - as happened at Windscale.
So, what happened was the transfer from one particular degree of freedom to all the others.

It's an odd use of "degree of freedom".  Wigner energy is potential energy stored as microscopic areas of mechanical stress when a neutron displaces an atom from its lattice position into a metastable trap. Wigner release is the conversion of that potential energy into phonons (i.e. heat) as the atom returns to a stable position. It's the "whole atom" equivalent of thermoluminescent electron trapping resulting from gamma radiation.   

[alancalverd]

My point was that Entropy is the log of something.  The log of something has no units.

S = -k_Blogp where k_B, Boltzmann's constant, has dimensions ML²T^-2K^-1, so S is far from dimensionless.

[Eternal Student]

Hi.

There's a point in the graphic where heat capacity is 4R/2. How should it be interpreted? Will additional heat energy be distributed evenly over 4 available degrees of freedom?

    I don't have any idea where that graphic came from.   It looks very simplified.  For a real substance you'd never get anything that perfect or perfectly symmetric at each transition zone betwen what is thought to be two states.
 
  Don't interpret it as suggesting that for a brief range of temperatures there was a state which supported 4 degrees - that's not the usual approach and not a good idea or model to have.

   A more reasonable way to interpret that location on the graph is that half of the substance is in a state where there are 5 degrees of freedom, while the other half of the substance is in a state where there are 3 degrees of freedom.       
   Similarly, all the other in-between positions (e.g. where it looks like 3.334 degrees of freedom exist) can be explained by varying the fraction of the substance in the two distinct states.

  Overall then , the heat capacity connects or relates to the average number of degrees of freedom that a particle would have.   Take a moment to think about this and you'll see that it will work:   If there are 2 particles, one with 3 deg. freedom,  the other with 5,   then   you need to deliver 8 units of energy to get the particles to increase the energy per degree of freedom by 1 unit,   this corresponds to a temperature increase of 1 unit -  that's precisely the same as  8 units of energy distributed to 2 particles with an average of 4 degrees of freedom each.
    The flat regions on the graph are where, to within a reasonable approximation, all the particles are in one state and have a set number of degrees of freedom   (3, 5 or 7 in your graph).

- - - - - - - - -
   I am a little curious about where you are going with this thread.   Is there something you think temperature should be?

Best Wishes.

[hamdani yusuf (OP)]

    I don't have any idea where that graphic came from.   It looks very simplified.  For a real substance you'd never get anything that perfect or perfectly symmetric at each transition zone betwen what is thought to be two states.

It's from wikipedia commons, which supposed to be a common knowledge and established science.

[hamdani yusuf (OP)]

   A more reasonable way to interpret that location on the graph is that half of the substance is in a state where there are 5 degrees of freedom, while the other half of the substance is in a state where there are 3 degrees of freedom.       
   Similarly, all the other in-between positions (e.g. where it looks like 3.334 degrees of freedom exist) can be explained by varying the fraction of the substance in the two distinct states.

  Overall then , the heat capacity connects or relates to the average number of degrees of freedom that a particle would have.   Take a moment to think about this and you'll see that it will work:   If there are 2 particles, one with 3 deg. freedom,  the other with 5,   then   you need to deliver 8 units of energy to get the particles to increase the energy per degree of freedom by 1 unit,   this corresponds to a temperature increase of 1 unit -  that's precisely the same as  8 units of energy distributed to 2 particles with an average of 4 degrees of freedom each.
    The flat regions on the graph are where, to within a reasonable approximation, all the particles are in one state and have a set number of degrees of freedom   (3, 5 or 7 in your graph).

I have considered your hypothesis. One of its implications is the increase of heat capacity would be more granular with fewer gas molecules. The chart would look like a stair.

[hamdani yusuf (OP)]

Wigner release is the conversion of that potential energy into phonons (i.e. heat) as the atom returns to a stable position.

Are all phonons heat? Are there some forms of phonon which are not heat?

[Bored chemist]

No, it was the release of Wigner potential energy that raised the temperature. Problem is that once you reach the annealing temperature you can initiate a chain reaction that outstrips the cooling capacity of the system - as happened at Windscale.
So, what happened was the transfer from one particular degree of freedom to all the others.

It's an odd use of "degree of freedom". 

It is an odd circumstance.
The point remains that the vibrations of atoms in a molecule are still heat energy.

[Eternal Student]

Hi.

It's from wikipedia commons, which supposed to be a common knowledge and established science.

   OK.  I'm not sure I've heard of it.  I'll guess it's a Wikipedia thing.   Do they explain it?

I have considered your hypothesis. One of its implications is the increase of heat capacity would be more granular with fewer gas molecules. The chart would look like a stair.

I'm not sure it would.
1.  No-one tries to consider a temperature for a small number of particles.   That graph looks simplified and idealised, presumably they are just communicating an idea.
2.  You can divide things up into segments of time if needed.  A particle can have 5 deg. freedom for half the time and 3 deg. of freedom for the other half of the time.  You'd still observe a heat capacity as if the particle had 4 degrees of freedom on average.   Temperature is only ever modelled as if you have an ensemble of particles,  a particle having a k.e. of 1 unit half the time and  1.5 units for the other half of the time can not be assigned a temperature.   However, the system can be modelled as if there was an ensemble of particles and the average k.e. of a particle was 1.25 units - that is something you can call a temperature.

Best Wishes.   

[alancalverd]

The point remains that the vibrations of atoms in a molecule are still heat energy.

Absolutely. But irrelevant to Wigner.

[hamdani yusuf (OP)]

It depends.

On what, exactly?

Guess.
or, even better, learn science.

It doesn't sound like a scientific answer.

[hamdani yusuf (OP)]

OK.  I'm not sure I've heard of it.  I'll guess it's a Wikipedia thing.

You can see the link by quoting the post.

[hamdani yusuf (OP)]

I am a little curious about where you are going with this thread.   Is there something you think temperature should be?

I just try to understand what temperature is by relating it with other things I already understood. The description by Wikipedia below requires the understanding of other concepts first. I want to understand how those concepts are related to each other consistently and useful to explain and predict observations and experimental results.

https://en.wikipedia.org/wiki/Temperature
Temperature is a physical quantity that expresses hot and cold or a measure of the average kinetic energy of the atoms or molecules in the system. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder or hotter. Temperature should not be confused with heat.

International Kelvin scale
Many scientific measurements use the Kelvin temperature scale (unit symbol: K), named in honor of the physicist who first defined it. It is an absolute scale. Its numerical zero point, 0 K, is at the absolute zero of temperature. Since May, 2019, its degrees have been defined through particle kinetic theory, and statistical mechanics. In the International System of Units (SI), the magnitude of the kelvin is defined through various empirical measurements of the average kinetic energies of microscopic particles. It is numerically evaluated in terms of the Boltzmann constant, the value of which is defined as fixed by international convention.[5][6]

Statistical mechanical versus thermodynamic temperature scales
Since May 2019, the magnitude of the kelvin is defined in relation to microscopic phenomena, characterized in terms of statistical mechanics. Previously, since 1954, the International System of Units defined a scale and unit for the kelvin as a thermodynamic temperature, by using the reliably reproducible temperature of the triple point of water as a second reference point, the first reference point being 0 K at absolute zero.[citation needed]

Historically, the triple point temperature of water was defined as exactly 273.16 units of the measurement increment. Today it is an empirically measured quantity. The freezing point of water at sea-level atmospheric pressure occurs at approximately 273.15 K = 0 °C.

The article says that temperature is a measure of the average kinetic energy of the atoms or molecules in the system. But we know that not all kinetic energy of the atoms or molecules are in the form of heat which contribute to the system's temperature. How they move also affects the temperature measurement of the system. Uniform rotation of a solid object can make it have a very high average kinetic energy. But usually it's not called a hot object.

https://en.wikipedia.org/wiki/Heat
In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter.[1][note 1]

Like thermodynamic work, heat transfer is a process involving more than one system, not a property of any one system. In thermodynamics, energy transferred as heat contributes to change in the system's cardinal energy variable of state, for example its internal energy, or for example its enthalpy. This is to be distinguished from the ordinary language conception of heat as a property of an isolated system.

The quantity of energy transferred as heat in a process is the amount of transferred energy excluding any thermodynamic work that was done and any energy contained in matter transferred. For the precise definition of heat, it is necessary that it occur by a path that does not include transfer of matter.[2]

Though not immediately by the definition, but in special kinds of process, quantity of energy transferred as heat can be measured by its effect on the states of interacting bodies. For example, respectively in special circumstances, heat transfer can be measured by the amount of ice melted, or by change in temperature of a body in the surroundings of the system.[3] Such methods are called calorimetry.

[Bored chemist]

The point remains that the vibrations of atoms in a molecule are still heat energy.

Absolutely. But irrelevant to Wigner.

So why did you introduce Wigner?
The point remains that this

So, what's your answer to this question : what is temperature?

A measure of the internal kinetic energy of a body.

is misleading because vibrational and rotational energy also contribute.

[Bored chemist]

It depends.

On what, exactly?

Guess.
or, even better, learn science.

It doesn't sound like a scientific answer.

Suggesting that someone guesses (i.e.  forms a hypothesis), then tests it is entirely scientific.

[Bored chemist]

For a real substance you'd never get anything that perfect or perfectly symmetric at each transition zone betwen what is thought to be two states.
 

It's a pretty good illustration of the real world.
The transition is smooth and more or less symmetrical because it's the behaviour of a large ensemble of things with 2 (or more) states.