# Reducing the entropy of a closed system

1. Oct 19, 2011

### antonima

Originally posted on sciforumsDOTcom by me (DRZion):

So I came up with a scenario which is simple enough for anyone to understand.

You take a fluid which is liquid at room temperature, but freezes to a become a solid denser than the liquid.

This is done to any amount of liquid at the surface of a pool of liquid. The energy required to freeze this liquid is x.

Now, the energy released as the solid sinks is just (Ds-Dl)vgh
where
Ds is density of solid
Dl is density of liquid
v is volume of the frozen solid
g is gravity
h is height

Since x is a constant and energy released scales with depth of the pool (h), there must exist a depth where x < energy released.

When the solid melts the temperature of the pool decreases, but it can draw this heat from the room, which is at room temp. Hence ambient heat -> gravitational potential.

What says Physics Forums?

2. Oct 19, 2011

### Mapes

This is not a closed system. If you freeze one part while keeping the rest at a constant temperature, you need to remove entropy.

(No alteration of this design is going to produce a system that spontaneously reduces entropy in a closed system. It's not worth your time to add additional features and tricks, unless you're going to learn more about the nature of phase transformations and entropy transfer under different pressures, for example.)

3. Oct 19, 2011

### antonima

This is false, its been proven mathematically that all systems have a probability of having their entropy reduced spontaneously.

Yes, I know, it takes more energy for the solid to melt at the bottom of the container because of the higher pressure. This is intuitive, the melting solid has a higher density than the fluid, so it literally has to lift all of the fluid above it when it expands during melting.

So, instead heat is pumped from the freezing portion to the bottom of the pool, closed system. Since the heat exchanger cannot be 100% efficient, lets say the heat released at the bottom is 2x, while the heat siphoned from the top is just x. There still exists a range of h values which result in a potential energy greater than 2x.

Last edited: Oct 19, 2011
4. Oct 19, 2011

### DaveC426913

How does a small probability of a spontaneous lowering in entropy for a short duration relate to designing a system to do this for a meaningful duration at will?

While it is true that system can spontaneously show a lowering of entropy for short durations, that does not falsify Mapes' assertion that you can't design it into the system.

5. Oct 19, 2011

### nasu

Do you mean heat pump rather than heat exchanger?
If so, what provides the energy to run the heat pump? For me is not clear, if you say that is a closed system.

6. Oct 19, 2011

### Mapes

If you're familiar with that intricacy of the Second Law, than you should also know that such a probability is indistinguishable from zero for any macroscale system.

You sure about that? Try running the numbers for a real solid.