I have recently started thermodynamics and am unclear about reason behind the direction of heat flow, which is usually stated as a given fact.
From the zeroth law of thermodynamics, originally, i thought temperature was defined as a physical property that
1. at thermal equilibrium, temperatures are equal
2. Heat always flows from higher to lower temperature
and so the direction of heat flow was just a matter of definition.
However, recently, I came across an argument based on the 2nd law of thermodynamics:
Heat flows from a system of higher temperature to one of lower temperature as the decrease in entropy of the hotter system due to a decrease, du, in internal energy is less than the increase in entropy of the colder system due to an increase, du, in internal energy, so the entropy of the universe increases.
So, is the direction of heat flow because of definition or the 2nd law of thermodynamics?
Best Answer
It is not just a matter of definition. It's a matter of observation. Heat is never observed to flow naturally or spontaneously from a low temperature substance to a high temperature substance. For that to happen, work must be done (as, for example, in the case of refrigerators and heat pumps.)
Before the second law was developed we had the first law. That law is a statement of conservation of energy. If heat heat were to flow from a cold to hot object, the heat lost by the cold object would equal the heat gained by the hot object and the first law would be satisfied. But since this never happens, a new law was needed that made such a flow of heat impossible .
Although the wording of the "argument" is rather awkward, at least to me, it is true that when heat transfers from the hotter system there is a decrease in both the entropy and internal energy (dU) of the hot system and there is an increase in both the entropy and internal energy of the cold system. The important distinction is internal energy is conserved but entropy is not, unless the heat transfer is "reversible".
The decrease in internal energy of the hot system exactly equals the increase in internal energy of the cold system, per the first law, for a total change in internal energy of zero. On the other hand, for any finite difference in temperature between the hot and cold system, the decrease in entropy of the hot system is less than the increase in entropy of the cold system, for a total entropy change greater than zero.
If the hot and cold systems are thermal reservoirs (constant temperature sources and receivers of heat), the entropy change of the hot system is
$$\Delta S_{H}=-\frac{Q}{T_H}$$
The entropy change of the cold system is
$$\Delta S_{C}=+\frac{Q}{T_L}$$
The total entropy change is
$$\Delta S_{tot}=+\frac{Q}{T_L}-\frac{Q}{T_H}$$
You will note that for all $T_{H}>T_{L}$, $\Delta S_{tot}>0$.
No. The natural direction of heat flow from hot to cold is an observable fact of nature. The second does not dictate nature. The second law reflects nature. The second law says that
$$\Delta S_{tot}=\Delta S_{sys}+\Delta S_{sur}\ge0$$
Where the equal sign applies to a reversible transfer of heat, i.e., when the difference between $T_H$ and $T_L$ approaches zero.
If heat flowed from cold to hot, the signs for the entropy changes in the first two equations above would be reversed, resulting in $\Delta S_{tot}<0$ in violation of the second law.
Hope this helps.