The Second Law of Thermodynamics

Introduction

No process is possible whose only result is the abstraction of heat from a system and the performance of an equivalent amount of work. There is no such thing as a 100% efficient system; it is impossible to turn all the heat absorbed into mechanical work, and that which is not used in mechanical work generates entropy. This defines entropy as a mathematical construct which only remains constant in a perfectly efficient (but hypothetical) closed thermodynamic cycle. The second law of thermodynamics defines the heat absorbed thus:

dQ > TdS

where dS is the change in entropy, and is therefore given by:

dS > dQ/T;

The change in entropy increases by this amount for a reversible process, and by a larger amount for an irreversible process (a complete and irretrievable departure from equilibrium, such as diffusion, explosions, etc., all of which are one-way process unless there is a significant amount of external intervention). This is because in the latter case the greater change in entropy is due to the nature of irreversibility, e.g., bonds being broken generating a dissociation energy. ΔS is always greater than zero with respect to the whole universe, so entropy itself of such an isolated system is always increasing. Thus for the change in internal energy we have:

dU = T dS - P dV

The state variables (P, V, T) define a unique state for a system.

The second law of thermodynamics places a direction of flow on heat energy. The energy flows from a hotter regions to colder regions to maintain thermal equilibrium.

A summary of the second law was given by C.P. Snow:

1. You cannot win. (energy and matter are conserved, so you cannot get something for nothing.)
2. You cannot break even (there is always an increase in entropy so you cannot even return to the same state.)
3. You cannot leave the game. (there is no way to escape rules 1 and 2 because it is impossible to reach absolute zero (see third law)