What are we storing when we cool water?

Suppose we use a heat pump to remove heat from a water tank at night when the ambient temperature is low. Exactly what are we storing? At first glance, the same amount of heat energy enters the heat pump at low temperature and leaves at high temperature. Entropy is heat divided by temperature. More entropy enters at low temperature than leaves at high temperature. The entropy inside the heat pump seems to be increasing.

Now that's not quite right. Energy also enters the heat pump in the form of electricity or work, and if the heat pump doesn't heat up, that additional energy must be leaving as heat. So the entropy inside the heat pump ends up constant.

But the entropy inside the insulated water tank is clearly decreasing. Heat is leaving and none is going in. So we are removing entropy from the water. We are storing an absence of entropy, or making a place where we can dump entropy later. Sometimes this is called "storing negentropy," or even "storing syntropy," but those terms are not widely accepted. So I will just say we are storing "cold" (with the "scare quotes") and link to this page.

Update:  I turned off "allow pings" because every time I link to this, I get a ping by email.  Maybe I won't get them anymore.

One Response to “What are we storing when we cool water?”

1. William Says:

A or Any Heat Engine produces or consumes mechanical energy as it moves thermal energy from one source or sink to the other.
A heat pump is a heat engine and requires or consumes mechanical energy to remove an amout of thermal energy from one place to be cooled to another at a higher temperature. This results in the work or mechanical input being converted into heat which is also rejected (delivered) to the high temperature region. It is also amenable to the limitations of Carnot.
Any heat pump or engine, can NOT store anyting with-in itself, NOTHING!
Unless I am badly mistaken, (I thought I made a mistake once and then I found out I was wrong about the whole thing), entropy cannot be calculated by a simple function but is either a point value for a specific state or is a mathematical integration. [It has been a long long time and I tend to forget a lot of detials. Please forgive me if I am wrong a second time. Have read the above article several times befpre and missed the point.]
Back to the ‘drawing board?

2. archimerged Says:

I agree with your description of heat engine and heat pump. I don’t think I said anything in contradiction to that.

If a heat pump or engine runs in a cycle returning to the identical state, then it can’t store anything or else the state is not the same. This is a matter of definition. You can make heat engines that store something temporarily and make short cycles that don’t return to the same point and only return to the same point rarely, for instance, once a day or once a year.

State space is a space with coordinates specifying all of the important properties of the system.

Entropy is a state function, its value independent of path through state space. You have to define its value at one point and at other points the entropy change is defined as path integral delta Q/T along any path whatever, because when a system is in a particular state it has a particular entropy (relative to the state where the entropy value is defined).