The Second Law and Entropy

The first law allows a huge number of transformations that nevertheless never happen in nature: on paper, nothing prevents a cooled cup of coffee from spontaneously warming up again by drawing heat from the surrounding air, while still respecting energy conservation. Yet this never happens. A rule is missing that sets the direction of transformations: this is the second law.

This law introduces a new state function, entropy, denoted S, which measures the microscopic disorder of a system. For an isolated system, entropy can only increase or remain constant over time: Delta S is always greater than or equal to zero. It strictly increases during an irreversible transformation (such as mixing, diffusion or friction) and remains constant during an ideal reversible transformation, a theoretical limit never exactly reached in reality.

This law gives physics an arrow of time: unlike Newton's laws, which are perfectly reversible in time, the second law distinguishes the past from the future. An ice cube melts in lukewarm water and the reverse never happens spontaneously; a gas spreads throughout the available volume and never compresses itself back into a corner on its own.

A misconception to correct: the entropy of a particular system can decrease — a refrigerator does cool its contents — but then the entropy of the whole universe, system plus surroundings, necessarily increases by more elsewhere. It is the total balance that can never decrease.

The pressure-volume diagram below illustrates a Carnot cycle, the theoretical benchmark for reversible engines: two isothermal transformations and two adiabatic transformations follow one another to bring the system back to its initial state, with no net change in entropy over a complete cycle.

P
^
6 |A
5 |    ___B
4 |        |
3 |        |___C
2 |D___
1 |    |_______|
  +--------------------------> V
       1   2   3   4   5   6

A -> B : (hot isotherm, at Tc: expansion)
B -> C : (adiabatic: expansion, cooling)
C -> D : (cold isotherm, at Tf: compression)
D -> A : (adiabatic: compression, heating)

Cycle traversed clockwise = (engine cycle, Carnot type)
Enclosed area of the cycle = W (net work supplied per cycle)