# Can you extract energy from "hot" things without a temperature differential?

I've been reading about extracting energy from heat, particularly Sterling engines. There's always a temperature gradient. Heat flows from the hot side to the cold side through the working fluid. As the temperature differential approaches zero the engine stops.

My question is that why do we even need a temperature differential? Even more broadly why do we use energy to cool things? Let's take a gallon of water at 50 deg C. Water has a specific heat of 4.18JdegC/g. Ignoring the heat of fusion and following Q = CMdT, just by virtue of it being "warm" (323 deg C above absolute zero) wouldn't the water "contain" 3780 * 4.18 * 323 = 5104 kJ of energy (3780 grams per gallon of water). Why couldn't you extract any of this energy as work and as a result of extracting the energy the water cools itself (it gives up energy, for every 3780*4.18 J extracted it should lower by 1 deg C). I'm invisioning the heated water (or anything heated above abs zero) as an energy sink or battery. Theoretically you should be able to extract 5104 kJ of energy from this 50 deg C gallon of water.

In the Sterling engine we could lower the cold side with liquid nitrogen but it takes energy to make this. In an AC system we spend energy to lower the temperature in the room. Since "cold" is the absence of "heat" or energy, shouldn't cooling things actually create energy for us (the hot things that earlier had energy imparted into them give up their energy to make work). It seems wasteful to just waste the heat on warming up something at a lower temperature differential such as the cool side of the Sterling engine or the ambient air by the condenser.

# The Ideal

The main problem is that all current technologies seem to waste a certain amount of energy on actually displacing some of the heat energy from A to B. If there were no such inefficiency, then we would in a sense obtain "free" energy as we could displace and focus an arbitrarily large amount of energy from a material into a finite space, and then use the laws of thermodynamics to power (e.g.) a stirling engine. If only there exists a structure that can naturally, without energy input, make one side cold and another warm. However, this gives us a contradiction.

Due to the second law of thermodynamics and the conservation of energy, this becomes impossible. As having a perfect "structure" that can transfer heat from A to B would violate these laws. It is required that energy be put into the system to actually perform the displacement. Therefore, even if said system is 100% efficient, energy is still put into the system such that no "free" energy is ever gained.

For reference (2nd Law of Th.) (wikipedia)

When two initially isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the entropies of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values.

# A Law

Unfortunately, the question is hard to answer:

My question is that why do we even need a temperature differential?

The reason is that the contrary is made impossible by a law. A law in physics and mathematics doesn't necessarily equate a theorem or theory. It only states "such is so." whilst a theory would actually explain "why such is so".

• As I stated in my answer, the second law of thermodynamics prevents us simply from doing so. Unfortunately there is no "why" to a law. If you are thinking about using the heat of a body to say propel an object, then the problem is the alignment of kinetic energy. You will be required to put energy into your system to align the molecules' kinetic energy such that it may purposeful.
– user44855
Jun 24, 2014 at 18:47
• There is a differential in the battery, the negative and positive pole. Unlike the water, most energy is stored as chemical potential. When the circuit is closed, the potential allows chemical reactions through oxidation and reduction to occur. The differential of the 2 poles causes the chemical reaction, and thus the amperage and power stream.
– user44855
Jun 24, 2014 at 18:53
• No energy is lost, there is simply no potential transfer from your tank to another system. Entropy therefore remains in a constant state. Therefore, energy in the system remains constant. However, you can not extract any energy using the thermoelectric effect or a stirling engine if you fail to find a suitable system to transfer between.
– user44855
Jun 24, 2014 at 19:03
• Thanks. I accepted your answer. I guess this is akin to dragging a jug of water up a mountain. It has a lot of energy (since it's high up), but relative to you you can only pour it onto the ground (small differential). If you can find a cliff to throw it off of you can extract the potential energy you imparted but other than that it's locked up. So you're telling me there is no way to extract the heat absent a suitable system to transfer to, Jun 24, 2014 at 19:17
• Worth mentioning Maxwell's demon Jun 25, 2014 at 12:49

A)
Without a temperature differential, there's no "hot". To say something is hot would mean it has a higher temperature than what you're comparing it with. eg. coconut oil, chocolate or gallium will melt in your hand because you are too hot for it to stay solid, but phosphorus or soap will stay solid because you're too cold for it.

Since 'hotness' is a measure of temperature differential, extracting energy from a point will change the temperature at that point. Also to extract (heat) energy, would mean to move it from a higher temperature to lower temperature (potential), just like any other form of energy, whether electricity or fluid dynamics.

In your case of "5104 kJ of energy", 100% of it could be extracted for work if the environment was at absolute zero and your extractor efficiency was at 100%.

B)
Re: "shouldn't cooling things actually create energy for us"

To cool anything, means to do some work, in this case 'cool'. Doing work, needs energy. So to cool anything will need energy, not create energy. As in A) above (the 1st part of your question), extracting (heat) energy from a point will cool it (reduce temperature), which requires work. So the energy potential you would create at that point by this extraction would be equal to the work you've done to extract the energy from that point, with 100% efficiency.