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Why does heat not flow spontaneously from a colder object to a hotter object?

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principles of physical science Figure 1: Data in the table of the Galileo experiment. The tangent to the curve is drawn at t = 0.6.

In the context of the principles of physical science, heat does not flow spontaneously from a colder object to a hotter object because such a process would violate the second law of thermodynamics.12

Specifically, the Clausius form of this law states that a cyclic transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible. This principle is fundamentally linked to the concept of entropy, which measures the unavailability of thermal energy for work and the degree of molecular disorder.123

For any spontaneous process in an isolated system, the total entropy must increase. If an amount of heat $Q$ flows from a reservoir at temperature $T_{1}$ to one at $T_{2}$ , the net change in entropy is defined as:13

$Δ S = \frac{Q}{T_{2}} - \frac{Q}{T_{1}}$

This value is positive only if $T_{1} > T_{2}$ . If heat were to flow from a colder body to a hotter one, the net entropy change would be negative, which is forbidden by the second law. While such a reversal is not impossible at the level of individual molecules, it is statistically so improbable in macroscopic systems that it is never observed.134