Laws of Thermodynamics and Properties

FE Exam Weight: Thermodynamics and Heat Transfer accounts for 9-14 questions (~10% of the exam). This section combines thermodynamic analysis with heat transfer modes.

The Laws of Thermodynamics

Zeroth Law

If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. (This establishes the concept of temperature.)

First Law (Conservation of Energy)

Closed System (no mass flow): $Q - W = \Delta U$ $q - w = \Delta u \quad (\text{per unit mass})$

Sign convention: Q positive into system, W positive out of system.

Open System (steady-state, steady-flow): $\dot{Q} - \dot{W}_s = \dot{m}\left[(h_2 - h_1) + \frac{V_2^2 - V_1^2}{2} + g(z_2 - z_1)\right]$

where:

• Q̇ = rate of heat transfer
• Ẇs = shaft power (work per unit time)
• h = specific enthalpy
• V = velocity
• z = elevation

Second Law

Kelvin-Planck: No heat engine can convert ALL heat into work (there must be waste heat).

Clausius: Heat cannot spontaneously flow from cold to hot without external work.

Entropy inequality: $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} \geq 0$

• = 0 for reversible processes

• 0 for irreversible (real) processes

Third Law

The entropy of a perfect crystalline substance approaches zero as temperature approaches absolute zero.

Thermodynamic Properties

Ideal Gas Relations

$PV = nRT = mR_{specific}T$

For air (standard values): cp = 1.005 kJ/(kg·K), cv = 0.718 kJ/(kg·K), k = 1.4, R = 0.287 kJ/(kg·K)

Thermodynamic Processes (Ideal Gas)

Phase Diagrams

T-s Diagram (Temperature vs. Entropy)

• Area under the curve = heat transferred (Q = ∫T ds)
• Horizontal line = isothermal process
• Vertical line = isentropic process

P-v Diagram (Pressure vs. Specific Volume)

• Area under the curve = work done (W = ∫P dv)
• Shows the two-phase dome (vapor dome)

P-h Diagram (Pressure vs. Enthalpy)

• Most useful for refrigeration cycle analysis
• Phase boundaries clearly shown