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3.10. Thermodynamics and Statistical Mechanics (TSM)

This area covers the laws of energy transfer, entropy, equilibrium states, and statistical foundations of macroscopic behavior. For Computing students, it provides the physical basis for energy-efficient system design, thermal management of hardware, and the statistical mechanics underpinning of machine learning algorithms.

Knowledge Area (KA)	CS Core	KA Core
3.10.1 Laws of Thermodynamics and State Functions	Elective
3.10.2 Kinetic Theory of Gases	Elective
3.10.3 Heat Engines, Entropy, and the Second Law	Elective

3.10.1. TSM/Laws of Thermodynamics and State Functions ↑ Back to top

Fundamental principles governing energy, heat, and work in 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
• Heat capacities \(C_V\) and \(C_P\) and their measurement and application

Learning Outcomes:
Core:

1. State the three laws of thermodynamics and give a physical interpretation of each [Familiarity]
2. Calculate work done by a gas during isothermal and adiabatic expansions [Usage]
3. Evaluate internal energy changes and apply the First Law to thermodynamic processes in computing systems [Assessment]

3.10.2. TSM/Kinetic Theory of Gases ↑ Back to top

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

• Derivation of macroscopic pressure from molecular momentum transfer
• Maxwell-Boltzmann speed distribution and its implications
• Equipartition theorem and degrees of freedom for monatomic and polyatomic gases
• Mean free path and its relevance to gas flow and vacuum systems

Learning Outcomes:
Core:

1. Describe the microscopic basis of pressure and temperature in an ideal gas [Familiarity]
2. Compute the rms and average molecular velocities using the Maxwell-Boltzmann distribution [Usage]
3. Apply the equipartition theorem to estimate heat capacities of gases and relate to energy storage in computing environments [Assessment]

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

Thermal efficiency limits, entropy generation, and the thermodynamic constraints, relevant to energy efficiency in data centers and computing hardware.
Topics:
Core

• Kelvin-Planck and Clausius statements of the Second Law and their implications
• The Carnot cycle and maximum efficiency \(\eta = 1 - T_c/T_h\)
• Clausius inequality and the thermodynamic definition of entropy
• Boltzmann's entropy formula \(S = k_B \ln \Omega\) and its statistical interpretation
• Landauer's principle: energy cost of irreversible computation and bit erasure

Learning Outcomes:
Core:

1. Explain the Second Law of Thermodynamics and its connection to the direction of spontaneous processes [Familiarity]
2. Calculate maximum thermal efficiency of a heat engine operating between two temperatures [Usage]
3. Apply Landauer's principle to analyze the thermodynamic cost of computing operations and memory erasure [Assessment]