5.1 Thermodynamic Laws and State Functions

5.1 Thermodynamic Laws and State Functions

Quick Answer: The zeroth law defines temperature via thermal equilibrium, the first law conserves energy, and the second law requires entropy of an isolated system never to decrease. State functions depend only on the current state; heat and work are path-dependent. Real processes are irreversible and generate entropy.

Domain B of the UPDA/MMUP Chemical exam (thermodynamics and phase equilibria — about 15% of this guide's planning allocation) rests on a small set of laws and property classifications. Phase equilibria, compressors, turbines, and flash calculations all assume you can state what is conserved, what can only increase, and which properties you may treat as path-independent.

Exam-Level Statements of the Laws

Zeroth Law

If body A is in thermal equilibrium with body B, and B is in thermal equilibrium with body C, then A is in thermal equilibrium with C. This transitivity justifies a temperature scale: systems in mutual thermal equilibrium share the same T. On the exam, the zeroth law is rarely a full calculation—it underpins why a thermometer reading is meaningful and why two streams at the same T can be mixed without a thermal driving force.

First Law (Energy Conservation)

For a closed system, a common engineering statement is:

ΔU = Q − W

where ΔU is the change in internal energy, Q is heat added to the system, and W is work done by the system. Some texts write ΔU = Q + W with W defined as work done on the system. Always check the sign convention in the stem; the physics is the same.

Key exam implications:

For open systems (steady flow), the first law is usually written on an enthalpy (and shaft work, KE, PE) basis—Chapter 4 energy balances. Domain B still uses the same conservation principle: energy is accounted for, not created or destroyed.

Second Law (Direction and Entropy)

The second law has several equivalent exam-level forms:

1. Clausius: Heat does not spontaneously flow from cold to hot without work input.
2. Kelvin–Planck: No engine can convert heat completely into work in a cycle while exchanging heat with only one reservoir (100% conversion of heat to work in a cycle is impossible).
3. Entropy form: For any real process, the total entropy of the system plus surroundings increases; for a reversible process it stays constant; it never decreases for an isolated system.

In symbols for an isolated system:

ΔS_isolated ≥ 0

with equality only for reversible processes. For a system alone, entropy can decrease if the surroundings increase by more (e.g., cooling a hot body), but entropy generation S_gen for the universe is always ≥ 0.

State Functions vs Path Functions

A state function depends only on the current thermodynamic state (typically specified by enough independent intensive variables, e.g., T and P for a single-phase pure fluid of fixed composition). Changing from state 1 to state 2, the change in a state function is the same regardless of path.

State functions (examples): U, H, S, G, A (Helmholtz), T, P, V, density, fugacity, chemical potential.

A path function depends on how the process is carried out. Heat and work are the classic pair: different paths between the same end states can exchange different Q and W even though ΔU is fixed by the end states (first law).

Practical rule: To compute ΔS between two states, invent a convenient reversible path connecting them (even if the actual process is irreversible). Entropy is a state function, so ΔS_system is path-independent; irreversibility shows up in S_gen, not in a failure of S to be a state property.

Intensive vs Extensive Properties

Dividing an extensive property by mass or moles yields an intensive specific or molar property (u, ĥ or H̄, etc.). Mixing rules and balances often use extensive totals; equilibrium criteria and equations of state are written with intensive variables.

Trap: Temperature and pressure are intensive—two tanks at the same T and P are not “twice as hot” when combined; their combined internal energy is the sum of the extensive U values.

Reversible vs Irreversible Processes

A reversible process can be reversed by an infinitesimal change, leaving no net change in system or surroundings. It is an idealization: no friction, no unrestrained expansion, no finite ΔT for heat transfer, quasi-static compression.

Irreversible processes include real compressors with efficiency < 100%, throttling (Joule–Thomson), mixing of different compositions, heat transfer across a finite temperature difference, and free expansion into vacuum.

Exam consequences:

• Work limits: For compression between two pressures, the reversible isothermal (ideal gas) or reversible adiabatic (isentropic) work is a benchmark. Real shaft work is larger in magnitude for compression (more power input) and smaller for expansion (less power output) than the reversible ideal for the same end states when compared fairly.
• Isentropic efficiency of turbines and compressors compares actual Δh to isentropic Δh—built on reversible adiabatic (S constant for the idealization) as the reference.
• Entropy generation quantifies irreversibility: larger S_gen means larger lost work opportunity.

Entropy Directionality for Common Processes

Adiabatic vs isentropic: Adiabatic means Q = 0. Isentropic means ΔS = 0. Only a reversible adiabatic process is isentropic. A real insulated compressor is adiabatic (approximately) but not isentropic.

Worked Conceptual Example: Classifying an Exam Statement

Stem style: “Steam expands irreversibly through an insulated turbine from superheated inlet to a lower pressure. Which statement is correct?”

Analysis:

1. Insulated ⇒ approximately adiabatic (Q ≈ 0).
2. Irreversible ⇒ not isentropic; s_out > s_in for a simple expansion if no heat loss (entropy increases along the actual path relative to the isentropic ideal).
3. Shaft work is less than the isentropic work output for the same inlet state and exit pressure (typical efficiency definition).
4. Enthalpy drop is smaller than the isentropic enthalpy drop for a turbine efficiency defined on Δh.

You do not need steam tables on every UPDA item, but you must classify: adiabatic ≠ reversible, H is a state function so h_in and the exit P (plus quality or T if given) fix possible exit states only with extra assumptions (efficiency, equilibrium, etc.).

System Types and Equilibrium

UPDA Chemical Exam Workflow

1. Identify system (closed/open/isolated) and whether the process is steady.
2. List known states (T, P, phase, composition) and which properties are state functions you can look up or compute from end states alone.
3. Apply first law with a stated sign convention for Q and W.
4. Apply second law qualitatively: is the process possible? Is S_gen zero or positive?
5. Never treat Q or W as state functions; never treat real adiabatic machines as automatically isentropic.

Common Traps

• Confusing ΔU = 0 (e.g., ideal-gas isothermal) with Q = 0 (adiabatic).
• Claiming S decreases for the universe in a spontaneous process (impossible).
• Using path-independent formulas for Q without specifying the path.
• Mixing intensive and extensive totals (adding temperatures, or forgetting to scale U with mass).
• Equating reversible with quasi-static only—reversibility also forbids finite driving forces for heat and composition.

Master these classifications before equations of state (Section 5.2) and before Cp/Cv and entropy generation calculations (Section 5.3). Phase equilibrium (Chapter 6) will reuse state functions G and chemical potential heavily.