Which law of thermodynamics states that heat cannot spontaneously flow from a…

Concept: thermodynamics rests on four laws, and each one fixes a different property of a system — one defines temperature, one conserves energy, one governs which changes can happen on their own, and one describes behaviour near absolute zero.

The law that governs the direction of a change is expressed through entropy: for an isolated system the total entropy can only increase or stay the same, so a process runs on its own only if it does not lower the total entropy of that system.

Applying that principle to heat shared between two bodies:

1. Take two bodies in thermal contact and isolated from their surroundings — a colder one at temperature Tc and a hotter one at temperature Th, with Th greater than Tc.

2. Suppose a small quantity of heat Q were to leave the colder body and enter the hotter one. The colder body loses entropy: ΔScold = − Q / Tc.

3. Over the same transfer the hotter body gains entropy: ΔShot = + Q / Th.

4. Adding the two gives the entropy change of the isolated pair: ΔStotal = Q ( 1 / Th − 1 / Tc ).

5. Since Th is greater than Tc, the quantity 1 / Th is smaller than 1 / Tc, so the bracket is negative and ΔStotal is less than zero.

6. A negative total entropy change is forbidden for a spontaneous process in an isolated system. Such a transfer therefore cannot happen by itself; it can be driven only by supplying external work, which is what a refrigerator or a heat pump does.

Cross-check and contrast with the other laws:

• Reversing the direction — the same heat Q passing from the hotter body to the colder one — gives ΔStotal = Q ( 1 / Tc − 1 / Th ), which is positive and therefore permitted. This is why heat drifts from hot to cold on its own.

• Transitivity of thermal equilibrium (the zeroth law) only lets temperature be defined and compared; it makes no claim about which way heat travels.

• Energy conservation, ΔU = Q − W (the first law), is satisfied exactly even by a cold-to-hot transfer, because the heat lost by one body equals the heat gained by the other, so this law alone cannot rule the transfer out.

• The low-temperature limit of entropy (the third law) describes what happens as absolute zero is approached and says nothing about the direction of a spontaneous exchange.

The restriction on the direction of spontaneous heat flow therefore comes from the second law of thermodynamics, in the form known as the Clausius statement: heat cannot pass by itself from a colder body to a hotter body.