# Basic understanding of entropy.

1. Oct 26, 2012

### Packocrayons

It may be a little advanced for me but I don't really understand how the total entropy can increase. If, for example you have an air conditioner in a room and the air conditioner is extracting the heat from the air in the room and transferring the excess heat to outside (the external air), wikipedia (although unreliable) claims that more heat is transferred to the external atmosphere than is extracted from the room. Following conservation of energy, this is not possible. So where is the excess heat coming from? Is it taking into account the electrical inefficiency of the wiring generating the extra heat?

2. Oct 26, 2012

### JustinRyan

Also heat caused by the current required to run the compressor, fans etc. Heat is also created at the power station where the current is generated. Entropy is only likely to increase for a CLOSED system.

3. Oct 26, 2012

### Staff: Mentor

The extra heat is coming from the work you are doing on the gas to compress it. There is a net amount of work done during each cycle. So the heat you remove from the room plus the work you do on the working gas is equal to the heat you reject to the external atmosphere. This is the main thing that is happening.

4. Oct 26, 2012

### JustinRyan

All the conservation laws still apply. Entropy is not heat. It is proportional to temperature but is more a measure of work or energy. Energy that has been converted to a form that can no longer be used to do work.

Two boxes contain the same amount of gas and the same amount of heat.
Only one box has a divider and there is a temperature difference accross the divider. One hot side and one cold side.
The other box has no divider and a homogeneous temperature throughout.

The box with the divider can be said to have less entropy than the box without because there is more "order" and the temperature difference can be used to do work.

5. Oct 27, 2012

### Studiot

Good morning packocrayons.

Taking note of this I will try to offer a simple explanation of entropy and I hope others will do the same. Much twaddle is promoted by those who have half understood the word and many fear it.

In fact is is really rather simple.

Entropy has the units of energy per degree (absolute temperature).
This provides a clue as to its nature.

Force and displacement, pressure and volume, stress and strain are pairs of physical quantities that can be brought together to measure some form of energy.

Since heat is a form of energy and temperature is not (edit: a form of energy) - a physical quantity was sought to pair with temperature to measure thermal energy.

This quantity is called entropy.
If we plot a graph of pressure v volume the area gives work energy
If we plot a graph of entropy v temperature the area gives heat energy

Such a graph is called an indicator diagram.

There are other pairs such as

EMF and Charge
Magnetic Field and Magnetic Moment
Surface Tension and Area

All of the variables are different and have significances of their own and all the products refer to particular forms of energy.

I hope this cuts entropy down to size for you.

Last edited: Oct 27, 2012
6. Oct 27, 2012

### JustinRyan

Thanks StudioT. After reading that I fear I am one who has half understood and I have studied thermodynamics. For all the twaddle I have heard that is the clearest description I have ever heard. :-)

7. Oct 27, 2012

### Studiot

Justin,

The coincidence of the statistical function called entropy and the thermal one is one of several amazing alignments in nature and our universe for which there is no obvious requiremet.

Some others are

The universality of the gravitational constant for all bodies

The fundamantal theorem of calculus.

go well

8. Oct 27, 2012

### Milan Nikolic

Nice explanation.

9. Oct 27, 2012

### Packocrayons

Okay so that's what was confusing me, I was looking at it simply: You extract the heat from one system and put it into another system, that heat increases for no logical reason and gets put into the second system at a higher rate. I wasn't thinking about the work done generating heat. I'm assuming the difference is fairly small?

10. Oct 27, 2012

### dipole

I'm sorry, but how does this explain to anybody what entropy is or means?

The classical definition, which is what you've described, is a purely mathematical definition with no real physical meaning behind it. From the statistical point of view, entropy has a far more profound meaning and is, in some sense, derivable.

For a given state of some system, entropy is the number of ways you can arrange the microscopic components of that system. When a system is in equilibrium, entropy is at a maximum.

That is what people mean when they say that entropy is a measure of "disorder". There is a very deep assumption that goes into the concept of entropy - that the behavior of microscopic particles are random, and because of this randomness the state of a system always tends to become more disordered with time. There is also a fairly deep connection with quantum mechanics, which also proclaims that microscopic particles behave in a random way.

In fact, there are some people who believe that statistical mechanics may be in some way more fundamental than quantum mechanics.

Entropy can be a little tricky to think about because it's different from other physical quantities we're used to, like volume, pressure, temperature etc...

11. Oct 27, 2012

### Studiot

Good evening, dipole.

What is the purpose of your intervention?

Do you really understand what this means?

Let me take a system comprising 6 black balls, six white balls and two egg boxes.

Can you calculate the entropy difference between the arrangement of 6 white balls in one box (and therefore 6 black in the other) and some other arrangement allocating all the balls to one box or the other. Please tell us the heat quantity required to change from one state to the other if all the balls and boxes are at the same temperature.