# Entropy: steam engines and fridges

1. Aug 20, 2009

### JanClaesen

A steam engine stove produces, say, 10 units of warmth, the second law states that not all warmth can be converted into work, so 8 units are converted into orderly energy, work, and 2 units aren't converted. Why did the entropy increase, since 10 units of warmth is more chaotic than 2?

A fridge cools something down, this cooling down, or decrease in entropy, is overcompensated by producing more warmth in the back of the fridge, so how is the total energy conserved, where does this 'extra' warmth come from?

Thanks!

2. Aug 20, 2009

### kyiydnlm

For the whole stove-work system, that "8 units" got higher thermodynamic probability.

Extra warmth comes from electricity.

3. Aug 20, 2009

### JanClaesen

Thermodynamic probability?

4. Aug 20, 2009

### bucher

For the steam engine, you need to consider the surroundings as well. Though 10 units of heat is more chaotic than 2, we are only considering the system at this point. Also, it is not just the heat that determines the entropy change but the change in temperatures of the system and surroundings. The 2 units of heat that weren't converted went into heating up the gears of the turbine through friction and/or was lost due to conduction to the surroundings. The energy became more irreversibly spread out. Because of that, the entropy increased.

5. Aug 20, 2009

### Mapes

10 units of warmth are not necessarily more chaotic than 2; in fact, you can't compare two energy values and say that one has higher entropy. If I have two reservoirs, one at high temperature $T_H$ and one at low temperature $T_L$, the same amount of energy (measured in Joules) will cause a larger increase in entropy (measured in Joules per Kelvin) when added to the low-temperature reservoir compared to the high-temperature reservoir.

And that's the whole idea of a heat engine: you produce 10 units of thermal energy, turn 8 into work, and send 2 as thermal energy to your low-temperature reservoir. Simultaneously, you produce $10/T_H$ units of entropy, turn none into work (because work carries no entropy) and output at least $2/T_L$ units of entropy to the low-temperature reservoir. $10/T_H$ and $2/T_L$ are the same number. So energy is conserved, and entropy is conserved (for a reversible engine) or increases (for a real engine).

Your other question can also be resolved by distinguishing energy and entropy. They are most definitely not the same thing.

6. Aug 20, 2009

### JanClaesen

Thanks, that was really clarifying
An increase in entropy is actually warmth being more spread, not necessarily a total increase in warmth?

7. Aug 20, 2009

### Mapes

Entropy increases with temperature, and energy increases with temperature, but you can't equate the two and argue that equal energy changes correspond to equal entropy changes.