Enthalpy & Reference States

See why H = U + PV is defined, why only ΔH matters, and how property tables pick an arbitrary zero.

Material & Energy BalancesChemical Engineering Year 1Free preview

⏱️ About 16 min

Why do flow problems almost always use enthalpy H instead of internal energy U — and why can't anyone tell you the 'absolute enthalpy' of a stream?

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The big idea: Enthalpy packages internal energy plus PV flow work into one convenient variable for flow processes, and only enthalpy differences (relative to a reference state) have physical meaning.

🎯 By the end, you'll be able to

Define enthalpy and explain why it is useful for flow systems
Explain flow work (PV work) and why it appears naturally in open systems
State why only changes in enthalpy are measurable
Interpret reference states used in property tables (e.g., steam tables)

📎 Helpful to know first

Forms of Energy & the First Law

Why Define Enthalpy?

In many chemical engineering devices (heat exchangers, pumps, turbines), material flows across the boundary. To push fluid into/out of a control volume, the surroundings must do flow work (also called PV work).

Rather than repeatedly writing 'internal energy plus PV terms', we define a new property:

H ≡ U + PV

This makes open-system energy balances compact and practical.

\[ H = U + PV \]

Definition of enthalpy. For a flowing stream, h = u + Pv (per unit mass) or h̄ = ū + Pv̄ (per mole).

Why H Is Natural for Flow Processes

Think of a fluid element entering a control volume. The upstream fluid must 'push' it in, doing work roughly equal to P·V. By absorbing that PV term into H, the energy carried by the stream is represented by its enthalpy.

That is why steady-flow equipment problems almost always use ΔH rather than ΔU.

⚠️ Only changes in enthalpy are measurable

You will sometimes see numbers like 'the enthalpy of steam is 2800 kJ/kg' in tables. That number is not an absolute truth — it is relative to an arbitrary reference state.

What is physically meaningful and measurable are differences: ΔH between two states.

Reference States in Property Tables

Steam tables and other property tables choose a convenient reference (a 'zero') for h and u. Different tables can use different zeros, but they will give the same Δh for the same change of state.

Practical rule: use a single, consistent source (one table set or one software package) throughout a calculation so your reference state cancels correctly.

📝 Worked example: A stream's enthalpy is reported as h₁ = 120 kJ/kg at state 1 and h₂ = 260 kJ/kg at state 2 (from the same property table). What is the specific enthalpy change Δh, and why is it meaningful even though the absolute values depend on a reference state?

Compute the change: Δh = h₂ − h₁ = 260 − 120 = 140 kJ/kg
Interpretation: Δh represents the energy change per kg between state 1 and state 2 under the chosen convention
Even if the table's zero were shifted by a constant C, both h₁ and h₂ would shift by C and Δh would stay 140 kJ/kg

✓ Δh = +140 kJ/kg; enthalpy differences are invariant to the arbitrary reference state.

✏️ Practice: Two different handbooks use different reference states and report h_A = 50 kJ/kg and h_B = 200 kJ/kg for the same two physical states A and B within each handbook. What is Δh from A to B (kJ/kg)?

kJ/kg

Solution

Compute within one consistent reference: Δh = h_B − h_A = 200 − 50 = 150 kJ/kg
Δh is meaningful; absolute h values are not, by themselves

Check your understanding

1. Enthalpy is defined as:

By definition, H = U + PV.

2. Which statement is true?

Tables choose an arbitrary reference; ΔH is what matters and is invariant to the chosen zero.

✅ Key takeaways

Enthalpy is defined as H = U + PV to simplify flow-process energy accounting
The PV term represents flow work that accompanies moving fluid across boundaries
Only enthalpy differences ΔH are measurable/meaningful; absolute H depends on a reference
Property tables use arbitrary reference states but give consistent ΔH values

➡️ Now that we know why enthalpy is the flow-friendly energy variable, we need a practical way to compute enthalpy changes with temperature — using heat capacities and sensible heat.

Want to test yourself on this? Try the Chemical Aptitude test →