At 0K (absolute zero) the atoms of a substance are stationary. They form a well ordered arrangement. When energy flows into a body its atoms vibrate, they become a less well ordered arrangement.

Boltzmann showed that changes in entropy of a body can be considered as a direct measure of changes in the disorder of the arrangement of the particles.

Consider a situation in which a hot body is brought into thermal contact with a cold body, for a short time.

We will imagine that the quantity of energy, Q, which flows from the hot to the cold body is so small that it does not significantly change the temperatures T₁ and T₂.

Each body will experience a change in the entropy of its particles.

The hot body experiences a decrease in entropy (a negative change) of magnitude S₁ = DQ/T₁

The cold body experiences an increase in entropy (a positive change) of magnitude DS₂ = DQ/T₂

The net change in entropy DS = DS₁ + DS₂.

Now T₂ < T₁ so DQ/T₂ must be greater than DQ/T₁.

Therefore, the net change in entropy due to this naturally occurring process must be greater than zero.

This leads to the following alternative statement of the second law of thermodynamics.
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