# Thermodynamics and thermoelectrics

1. Aug 12, 2012

### hercules68

Thermoelectrics convert heat to electric power (albeit a meager amount), It reduces the entropy of a system.

Does this mean that it defies the second law of thermodynamics !

2. Aug 12, 2012

### Studiot

Have you done any calculations to substantiate this claim?

3. Aug 12, 2012

### jahaan

Do you mean it reduces the entropy of an isolated system, consisting of a circuit and a heat source?

Remember that the 2nd law only states the entropy of a fully isolated system can't drop. Is the system you're imagining fully isolated? Also, have you taken into account the entopy of the electrons that are set in motion?

4. Aug 12, 2012

### Studiot

Electrical work must also be done in such a circuit.

5. Aug 13, 2012

### Darwin123

No. A thermoelectric refrigerator, like all other refrigerators, uses work to move entropy from a low temperature area to a high temperature area. Moving entropy with work does not violate the second law of thermodynamics.
The second law of thermodynamics states that the total entropy of a closed system can not spontaneously decrease. Thus, total entropy can not be destroyed. However, entropy can be moved.
A thermoelectric cooler would work like this. Let us suppose that there is a cold reservoir and a hot reservoir that are connected through the cooler. Electric current would flow into the cooler against a voltage gradient. Thus, the electric charges will do work on the system. Entropy will flow then flow from the cold reservoir to the hot reservoir.
The transport of entropy in this case is not spontaneous because it would not happen without the work done by the electric charges. The efficiency of such a system would be less than an equivalent Carnot refrigerator if it replaced the thermoelectric refrigerator.
Note that the thermoelectric refrigerator creates entropy. Although the temperature of the cold reservoir decreases, the temperature of the hot reservoir increases still more. The resistance of the wires and contacts outside the thermoelectric substance will result in heating that has nothing to do with the thermoelectric substance.
Here is a link to a Wikipedia article on thermoelectric cooling. Note that the thermoelectric cooler is no more that 10% as efficient as a Carnot refrigerator. Thus, it can’t decrease the total energy of the universe. In fact, it would increase the total entropy of the universe.

http://en.wikipedia.org/wiki/Thermoelectric_cooling
“Thermoelectric junctions are generally only around 5–10% as efficient as the ideal refrigerator (Carnot cycle), compared with 40–60% achieved by conventional compression cycle systems (reverse Rankine systems using compression/expansion). Due to the relatively low efficiency, thermoelectric cooling is generally only used in environments where the solid state nature (no moving parts, maintenance-free, compact size) outweighs pure efficiency.”

6. Aug 13, 2012

### Studiot

Please note the difference between what jahaan has said and what Darwin has said.
Neither are full expositions of the second law.

It can be very confusing when different people talk of different things about the same subject.

There is a difference between a closed system and an isolated system.

A closed system might be some material that has all its heat extracted from it and so has reached absolute zero temperature and thefore has zero entropy.

The second law says that you can only achieve this by doing work.

Of course in an isolated system you cannot extract heat since no energy of any kind can pass the boundary.

7. Aug 13, 2012

### Darwin123

That is why I included the word "spontaneously". If one can only achieve "this" without doing work, then "this" isn't spontaneous.
An isolated system also can not do work, or have any work done on it. An isolated system can not exchange matter or energy with an outside system.

8. Aug 14, 2012

### Studiot

@Darwin

Please also note I didn't say either use of the second law was incorrect, just incomplete. Yes you need the spontaneous condition for your version.

9. Aug 27, 2012

### hercules68

Lets say that the resulting electric energy is stored in a battery . . now how does the entropy increase or even remain same

10. Aug 27, 2012

### hercules68

No , this is a qualitative analysis

11. Aug 27, 2012

### Studiot

So have you included the entropy of the surroundings from where the heat comes?

12. Aug 27, 2012

### hercules68

Yes thats were the heat comes from

13. Aug 27, 2012

### Studiot

Unfortunately you misunderstood.

I asked if you have included the entropy of the surroundings in your calculation?

14. Aug 27, 2012

### Staff: Mentor

Herculese, the point after heat addition in any thermodynamic cycle is the point of maximum entropy: it always decreases after that. You can't ignore the input if you want to analyze the whole cycle. That logic would make a hydroelectric plant a violator of the first and second laws.

15. Aug 27, 2012

### Darwin123

The thermoelectric cell won't work if the surroundings have a uniform temperature. So there heat can't come from "the" surroundings.
To make electricity, one side of the thermoelectric cell has to be at a different temperature than the other side of the thermoelectric cell. The material of the thermoelectric cell itself has to have a small thermal conductivity.
Heat energy is conducted from the high temperature side of the thermoelectric cell to the low temperature side of the thermoelectric cell. Thus, the increase in entropy on the low temperature side has to be larger than the decrease in entropy on the high temperature side. Thus, the total change in entropy on both sides of the cell is positive. The entropy of the universe has increased!
Let ΔE be the energy passing from one side to the other side of the thermoelectric cell.
ΔS=ΔE/T1-ΔE/T2
If T2>T1,then ΔS>0.
Entropy has increased!
The thermoelectric cell can't work if T1=T2. I hypothesize that you think T1=T2. This isn't true.