[alancalverd]

Would that be 0.3010 or 0.6931? Or does it mean log₂ of any number you can think of?

[Spring Theory]

Would that be 0.3010 or 0.6931? Or does it mean log₂ of any number you can think of?

0.3010

[Spring Theory]

My elegant description of temperature

It may be elegant, but it isn't much use.
Do you think that you can clearly explain the concept of entropy changes without using temperature in your explanation?

Entropy is the probability function of the potential states of a system.  It directly relates to the information you know about a system. 

If you know everything or the exact state of the system, then it has zero entropy. If you only know there are a potential number of states, n, and there is an equal probability of each state, then the entropy is proportional to n.

Essentially, entropy increases with your ignorance of the state of a system, but is usually used in calculations as a property of the system.

[hamdani yusuf (OP)]

Would that be 0.3010 or 0.6931? Or does it mean log₂ of any number you can think of?

0.3010

Why do you use base 10 instead of e?
What's your dimensional analysis?

[hamdani yusuf (OP)]

Temperature is the amount of energy required to change the entropy by one bit.

So the entropy of an object at constant temperature is continually changing?  Welcome to the world of Hamdani Yusuf!

I disagree with the statements above. But of course you are free to put everyone who disagree with you into the same category, but the more appropriate name would be the world of non-Alan Calverd.

[hamdani yusuf (OP)]

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

A measure of the internal kinetic energy of a body.

You need to specify what you mean with internal and kinetic, in contrast to external and potential.

[Bored chemist]

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

A measure of the internal kinetic energy of a body.

You need to stop repeating the error that it's kinetic energy that counts.
It's any form of energy.
However, when a body has a well defined temperature the energy per degree of freedom will be the same anyway.

[Bored chemist]

Temperature is the amount of energy required to change the entropy by one bit.

So the entropy of an object at constant temperature is continually changing?  Welcome to the world of Hamdani Yusuf!

The gradient is d height/ d distance .
That doesn't mean that all hills are moving.
That's not H Y's world, nor S T's world.
It's only in your world.

[Bored chemist]

Why do you use base 10 instead of e?

That might be the best question H Y has ever asked.

[alancalverd]

It's any form of energy.

Er, no. The potential energy of a strained lattice may be enormous, but as that can't be transferred by thermal conduction to another body, it doesn't affect its temperature.

There's a discussion elsewhere about dissolving a stressed spring.

[alancalverd]

Temperature is the amount of energy required to change the entropy by one bit.

So the entropy of an object at constant temperature is continually changing?  Welcome to the world of Hamdani Yusuf!

The gradient is d height/ d distance .
That doesn't mean that all hills are moving.
That's not H Y's world, nor S T's world.
It's only in your world.

So if T>0, by ST's statement there is plenty of available energy in the system to change its entropy, and nothing to stop it.

[Spring Theory]

Would that be 0.3010 or 0.6931? Or does it mean log₂ of any number you can think of?

0.3010

Why do you use base 10 instead of e?
What's your dimensional analysis?

Entropy is dimensionless. This is why temperature is in units of energy.

Information theory uses base 2, some physics use natural log.  I just picked base 10.  You can pick what ever you want to be defined as one bit.  Any conversion factor can be absorbed by the constant I set to 1. That's not the important part.

Entropy is the average of the logarithm of the probability distribution of the states.



Where S is the entropy and P(i) is the probability of the i'th state. The negative sign is because the probability is always less than or equal to 1. This becomes:



When you add up each state probability value.

[alancalverd]

This is why temperature is in units of energy.

No. The mean energy of a particle within a body is k_BT  where k_B is the Boltzmann constant, whose dimensions are joules per kelvin.

Entropy is dimensionless.

No. The dimensions of entropy are joules per kelvin.

[Spring Theory]

So for example is you know the state of the system, then that state has a probability of 1 and all the other states have zero probability, the entropy becomes (remember Boltzmann's constant is one):

If the are m states equally probably, then the entropy is:

And you now have the generalization of what entropy is.  It is the logarithm (you can pick your base) of the variation of different states a system can have.

[Spring Theory]

This is why temperature is in units of energy.

No. The mean energy of a particle within a body is k_BT  where k_B is the Boltzmann constant, whose dimensions are joules per kelvin.

Entropy is dimensionless.

No. The dimensions of entropy are joules per kelvin.

Kelvin = Energy

[hamdani yusuf (OP)]

There's a discussion elsewhere about dissolving a stressed spring.

That's interesting. Can someone give the link?

[hamdani yusuf (OP)]

Kelvin = Energy

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

[Bored chemist]

It's any form of energy.

Er, no. The potential energy of a strained lattice may be enormous, but as that can't be transferred by thermal conduction to another body, it doesn't affect its temperature.

There's a discussion elsewhere about dissolving a stressed spring.

The point remains  that vibrational + electronic energy is also part of thermal energy.

"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...

As I said...

However, when a body has a well defined temperature the energy per degree of freedom will be the same anyway.

[alancalverd]

"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.

[hamdani yusuf (OP)]

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?