Revision sheet: Thermodynamics of Equilibrium Systems

Thermodynamics of Equilibrium Systems - Revision Sheet

1. 📌 Essentials

• System types: closed (no matter exchange), open (matter exchange), isolated (no energy or matter exchange).
• Equilibrium: no mac change; requires uniform pressure and temperature.
• State variables: extensive (U, V), intensive (p, T); path-independent.
• Equation of State: ideal gas: pV = nRT; Van der Waals: (p + a(n/V)^2)(V - nb) = nRT.
• Transformations: quasi-static, reversible, adiabatic, isenthalpic, isobaric, isochoric.
• Phase transitions: latent heat, critical point, triple point; phases: solid, liquid, gas.
• First law: ΔU = W + Q; energy conservation.
• Cycle: initial and final states identical; net energy change zero.
• Maximum efficiency: Carnot cycle: η = 1 - Tf/Tc.
• Latent heat: energy absorbed/released during phase change (e.g., vaporization ≈ 2257 kJ/kg---

2. 🧩 Key Structures & Components

• System boundary — separates system from surroundings.
• States of matter — solid, liquid, gas.
• Phase diagram — shows phases, coexistence lines, critical point, triple point.
• Equation of State — relates p, V, T for gases.
• Latent heat — energy during phase change at constant T and P.
• Energy forms — internal energy (U), enthalpy (H), kinetic, potential.
• Process types — isothermal, adiabatic, isobaric, isochoric.
• Cycle components — heat source, heat sink, work output.

3. 🔬 Functions, Mechanisms & Relationships

• Energy balance: ΔU = W + Q; applies to closed systems.
• Work in quasi-static process: W = -∫ p dV.
• Enthalpy: H = U + pV; useful at constant pressure.
• Adiabatic process: no heat transfer (Q=0); pV^γ = constant.
• Phase change: occurs at constant T and P; involves latent heat.
• Cycle operation: energy input as heat, output as work; efficiency limited by Carnot.
• States connected by equations: p, V, T define the system; phase transitions occur at specific T, P.
• Energy transfer: heat flows from hot to cold; work done by system depends on process path.

4. 📊 Comparative Table

Item	Key Features	Notes / Differences
Ideal Gas	pV = nRT; no interactions	Simplified model, accurate at low P, T
Van der Waals Gas	(p + a(n/V)^2)(V - nb) = nRT	Accounts for molecular interactions
Reversible Process	No entropy production; idealized	Maximum work obtainable
Irreversible Process	Entropy increases; real processes	Less work, more entropy production
Isothermal	Constant T; work = -nRT ln(Vf/Vi)	ΔU = 0
Adiabatic	No heat transfer; pV^γ = constant	T ∝ V^(γ-1)
Isobaric	Constant pressure; work = -p(Vf - Vi)	ΔH = Qp
Isochoric	Constant volume; no work, heat changes U or H	ΔU = Qv

5. 🗂️ Hierarchical Diagram (ASCII)

Thermodynamic System
 ├─ System Types
 │    ├─ Closed
 │    ├─ Open
 │    └─ Isolated
 ├─ Equilibrium Conditions
 │    ├─ Mechanical (p uniform)
 │    └─ Thermal (T uniform)
 ├─ State Variables
 │    ├─ Extensive: U, V
 │    └─ Intensive: p, T
 ├─ Processes & Transformations
 │    ├─ Quasi-static
 │    ├─ Reversible
 │    ├─ Adiabatic
 │    ├─ Isothermal
 │    └─ Isobaric / Isochoric
 └─ Phase Diagram & Transitions

6. ⚠️ High-Yield Pitfalls & Confusions

• Confusing reversible with quasi-static processes; all reversible are quasi-static, but not all quasi-static are perfectly reversible.
• Mistaking latent heat as energy change in temperature; it involves phase change energy, not temperature change.
• Overlooking the entropy increase in irreversible processes.
• Assuming ideal gas law applies at high pressures or low temperatures.
• Confusing enthalpy (H) with internal energy (U); H = U + pV.
• Misinterpreting the critical point as a phase transition; it's the end point of the liquid-gas coexistence line.
• Forgetting that cycle efficiency cannot reach 100%; limited by Carnot efficiency.
• Overestimating the work obtainable in real processes compared to ideal reversible cycles.

7. ✅ Final Exam Checklist

• Define and distinguish between system types: open, closed, isolated.
• State the equilibrium conditions: uniform p and T.
• Write the equation of state for ideal and Van der Waals gases.
• Explain the first law of thermodynamics and its application.
• Describe quasi-static, reversible, adiabatic, isothermal, isobaric, and isochoric processes.
• Identify phase transitions and latent heats.
• Draw and interpret phase diagrams: triple point, critical point, coexistence lines.
• Calculate work, heat, and energy changes during processes.
• Derive and understand cycle efficiencies, especially Carnot.
• Recognize the significance of entropy and the second law implications.
• Apply energy balances to open and closed systems.
• Understand the limitations of idealized models versus real systems.

End of Revision Sheet