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4.12. Thermodynamics and Statistical Mechanics (TSM)

Thermodynamics and Statistical Mechanics bridge microscopic properties of matter and macroscopic engineering observables. This area covers the laws of energy transfer, entropy, equilibrium states, and heat engine cycles essential for energy systems and thermal engineering.

Knowledge Area (KA)	Core Tier1	Core Tier2
4.12.1 Laws of Thermodynamics and State Functions	1	1
4.12.2 Kinetic Theory of Gases	1	1
4.12.3 Heat Engines, Entropy, and the Second Law	Elective

4.12.1. TSM/Laws of Thermodynamics and State Functions  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Fundamental principles governing energy, heat, and work in engineering thermodynamic systems, and the mathematical definition of state variables.
Topics:
Core

• Zeroth Law of Thermodynamics and temperature equilibrium
• First Law of Thermodynamics: \(dU = dQ - dW\) for engineering systems
• Enthalpy \(H = U + PV\) and its role in flow processes and chemical reactions
• Heat capacities \(C_V\) and \(C_P\) and their engineering measurement and application
• Adiabatic processes and isentropic flow conditions in turbomachinery

Learning Outcomes:
Core:

1. Calculate work done by a gas during isothermal and adiabatic expansions in engineering cycles [Usage]
2. Evaluate internal energy changes and apply the First Law to engineering thermodynamic processes [Assessment]
3. Apply Mayer's relation to determine heat capacity ratios for engineering working fluids [Usage]
4. Analyze isentropic flow conditions in engineering nozzles and turbines [Assessment]

4.12.2. TSM/Kinetic Theory of Gases  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Microscopic model of gases relating molecular motion to macroscopic engineering properties such as pressure, temperature, and transport coefficients.
Topics:
Core

• Derivation of macroscopic pressure from molecular momentum transfer
• Maxwell-Boltzmann speed distribution and its engineering implications
• Equipartition theorem and degrees of freedom for monatomic and polyatomic gases
• Mean free path and its relevance to gas flow and vacuum engineering
• Transport phenomena: viscosity, thermal conductivity, and diffusion in engineering gases

Learning Outcomes:
Core:

1. Compute the rms and average molecular velocities for engineering working gases [Usage]
2. Interpret the Maxwell-Boltzmann distribution and its temperature dependence for engineering applications [Assessment]
3. Calculate mean free path and relate it to viscosity in gas-dynamics engineering problems [Usage]
4. Estimate thermal conductivity and viscosity of a gas from kinetic theory for engineering design [Assessment]

4.12.3. TSM/Heat Engines, Entropy, and the Second Law ↑ Back to top

Thermal efficiency limits, entropy generation, and the thermodynamic constraints governing engineering heat engines and refrigeration cycles.
Topics:
Core

• Kelvin-Planck and Clausius statements of the Second Law and their engineering implications
• The Carnot cycle and maximum efficiency \(\eta = 1 - T_c/T_h\)
• Clausius inequality and the thermodynamic definition of entropy
• Analysis of engineering cycles (Rankine, Brayton, Refrigeration) using \(T\)-\(S\) diagrams
• Boltzmann's entropy formula \(S = k_B \ln \Omega\) and its engineering interpretation

Learning Outcomes:
Core:

1. Calculate the maximum thermal efficiency of an engineering heat engine operating between two temperatures [Usage]
2. Evaluate entropy generation in irreversible engineering processes such as heat transfer across a finite temperature difference [Assessment]
3. Analyze the thermodynamic performance of Rankine and Brayton cycles using \(T\)-\(S\) diagrams [Usage]
4. Compute entropy changes from microscopic state counts for simple engineering systems [Usage]