Entropy Balance

Entropy is an extensive property, like mass and energy, that can be used to characterize the state of thermodynamic systems at equilibrium. The entropy of a system changes as a result of a process but it is not a conserved quantity. Generation of entropy, S_gen, is equal to the entropy change of the universe, i.e.,

S_gen = ΔS_universe

         =ΔS_system + ΔS_surroundings  ≥  0               (1)

ΔS_system may be less than zero. However, ΔS_universe is either zero (reversible process) or greater than zero (irreversible process).

For an open system (both mass and energy is exchanged with surroundings), the rate of entropy generation is expressed as:

Ṡ_gen = Ṡ_system + Ṡ_surrounding              (2)

The rate of entropy change of the system is expressed as:

The entropy of the surroundings may change through two ways: (i) mass flow, (ii) heat transfer. Note that entropy transfer has nothing to do with work. Thus,

This is also known as the entropy balance. Note that dQ_surr = − dQ_sys and dS_gen ≥ 0.

Simplifying Eq. 6 for different types of systems is given below:

Isolated Systems

Since there is no exchange of mass and energy between the system and its surroundings, Eq. 6 simplifies to:

Closed System

Since there is no exchange of mass between the system and its surroundings, i.e., d_min = dm_out = 0, Eq. 6 simplifies to:

Steady State System

Noting that:

d_min = dm_out = dm                         and

                                                                   d(mŜ)_sys = 0

 Equation 6 simplifies to: