Enthalpy, Entropy, And The Second Law of Thermodynamics

Enthalpy, entropy and the second law sit on top of the first-law energy balance. Enthalpy is u + pv. Entropy change along a reversible path is dq_rev / T. The second law says the entropy of an isolated system does not fall. This page then covers internal energy, cyclic and arbitrary processes and reversibility.

• Internal Energy and First Law of Thermodynamics
• The cyclic and arbitrary process of a system
• Reversibility and Irreversibility
• Entropy and Enthalpy
• Second Law of Thermodynamics

Internal Energy and First Law of Thermodynamics

Internal energy (u) is the microscopic energy stored in a system’s molecules. The first law says that energy is not created or destroyed, so u changes only when heat or work crosses the boundary. That statement is the First Law of Thermodynamics for a closed system using the engineering sign convention below.

In that equation u is internal energy per unit mass and q and w are heat and work per unit mass. The page uses the common engineering signs, not the IUPAC ΔU = Q + W convention:
dq > 0 (considered as positive) ⇒ Heat transfer to the system
dq < 0 (considered as negative) ⇒ Heat transfer from the system dw > 0 (considered as positive) ⇒ work done by the system
dw < 0 (considered as negative) ⇒ work done on the system

Cyclic and Arbitrary Process of a System

A useful form of the first law appears when the process is a cycle.

Integrate that differential around the closed path.

A cyclic process returns the system to its initial state after a sequence of heat and work exchanges. Because u is a state function, the net change of internal energy on that loop is zero.

Two consequences follow:

1. Integration of any state property differential is the difference of its limits.
2. Final state is same as the original state and there is no change in internal energy of the system.

Thus when

i and f mark the initial and final internal energy. For a cycle those states coincide, so the substitution into equation (1) is

Equation (2) says the net work done by the system equals the net heat absorbed, under this sign convention. Engineering thermodynamics develops systems and processes further.

Arbitrary Process of a System

For any process, not only a cycle, the same first-law statement integrates to equation (1) in finite form.

Here q and w are net heat and net work for that process, and uf and ui are the final and initial internal energy. If the system is rigid and adiabatic (w = 0, q = 0), u does not change. That result is consistent with equation (2) on a cycle, where the net heat still equals the net work.

Reversibility and Irreversibility

A process takes the system from one state to another, so properties such as pressure, volume, enthalpy, temperature and entropy change. The second law then splits processes into reversible ideals and the irreversible processes that occur in plant equipment.

If temperature (t) and pressure (p) change only by infinitesimal amounts while the system is in a process, the path is a sequence of near-equilibrium states and approaches reversibility.
The process is internally reversible if the system can be restored by reversing the path.
It is externally reversible if the surroundings can also be restored in reverse sequence.
A fully reversible process is reversible both internally and externally.
Engineers use that reversible limit as the yardstick for a real machine: cut friction, unrestrained expansion and finite-temperature heat transfer to raise efficiency toward that bound.

Irreversibility

A process that cannot meet those reversibility conditions is irreversible.
The combined system plus surroundings cannot be restored to the initial state. Entropy of that isolated pair rises; it does not have to rise “sharply,” and a closed system can lose entropy if it rejects heat. Friction, unrestrained expansion, mixing and heat transfer across a finite temperature difference are the usual causes. Reducing those effects raises thermal efficiency.

Entropy and Enthalpy

Entropy and enthalpy are state properties like internal energy. Specific entropy (s) is in kJ/kg·K. Along a reversible path ds = dq_rev / T, and that relation is the usual starting point for the second law.

Where q_rev is heat transferred along a reversible path.
Enthalpy (h) is the state property defined as

where h is specific enthalpy, u is specific internal energy, v is specific volume and p is pressure. The pv term is the flow work needed to push the fluid’s volume into the surroundings.
From equation (1)

Therefore

By differentiating the eq (4) and substituting it in above equation, then

The first of those two relations ties reversible entropy change to internal energy and volume. The second ties it to enthalpy and pressure. Every quantity in them is a state property, so entropy is a thermodynamic property as well.

Second Law of Thermodynamics

The Second law of thermodynamics limits which processes can occur, not how much energy is conserved. The 2^nd law accounts for irreversibility: friction, heat leak and mixing that the first law still counts as energy.
Everyday plant processes are irreversible in that sense.
A convenient statement uses entropy:
For a reversible heat addition, the entropy change of the system is the heat added divided by the absolute temperature at the boundary.

The second law then states that the entropy of an isolated system does not decrease. A closed system that rejects heat can lose entropy; the surroundings gain more. The boxed summary that entropy in a closed system never decreases mislabels that isolated-system rule.
OR
An isolated universe tends toward a state of greater entropy, often described as greater disorder