Internal energy

62 topics across 6 chapters

Chapter 1

Thermodynamic foundations (what U is and how systems are defined)

Systems, surroundings, boundaries (what you’re analyzing)

2 subtopics

Define system vs surroundings; choose a clear boundary and interactions

Closed vs open systems; control mass vs control volume

Heat and work as energy transfer (not “stored” in the system)

3 subtopics

Distinguish heat (Q) and work (W) from stored energy (U)

Sign conventions for Q, W, and ΔU (avoid sign mistakes)

Catalog common work modes: boundary (P–V), shaft, electrical, surface tension

State variables and equilibrium (why U is a state function)

2 subtopics

Extensive vs intensive properties; specific internal energy u = U/m

Equilibrium and quasi-static processes (when state relations apply)

P–V diagrams and process paths (reading thermodynamic “stories”)

Units and conventions used in thermodynamics (kJ/kg, kPa, etc.)

Chapter 2

Microscopic interpretation (molecules → macroscopic U)

Molecular energy components that make up internal energy

2 subtopics

Identify translational, rotational, vibrational, and electronic contributions

Separate internal energy from bulk kinetic and gravitational potential energy

Degrees of freedom and heat capacity (why U depends on T)

2 subtopics

Equipartition theorem (where it works and where it fails)

Connect Cv and Cp to microscopic degrees of freedom (qualitative + basic math)

Intermolecular potential energy (why liquids/solids differ from gases)

Statistical mechanics link: U as an average over microstates

Chapter 3

First law & energy accounting (how U changes)

First law for closed systems (control mass)

3 subtopics

↗ Sign conventions for Q, W, and ΔU (avoid sign mistakes) (see Chapter 1)

Write and use dU = δQ − δW and ΔU = Q − W (with consistent signs)

Special cases: isochoric, adiabatic, and isothermal interpretations of ΔU

Computing heat/work to find ΔU (recipes and examples)

2 subtopics

Boundary (P–V) work: W = ∫ P dV and how to compute it from paths

Non-P–V work: electrical, shaft, stretching, and “other” work terms

Enthalpy and flow work (why engineers switch from U to H)

2 subtopics

Use H = U + PV; understand “flow work” and why tables often give h

Constant-pressure heating/cooling: relate ΔH to heat transfer in many cases

Steady-flow energy equation (SFEE) for devices (turbines, nozzles, compressors)

Chapter 4

Models & materials (how U behaves in common substances)

Ideal gas internal energy model

2 subtopics

For an ideal gas: u = u(T) only; understand what that implies for ΔU

Calorically perfect vs variable-Cv gases; compute u(T) from Cv(T)

Real fluids & equations of state (how u depends on T and v for real substances)

Incompressible liquids/solids (common approximations for u(T))

Phase change & two-phase mixtures (why tables matter)

2 subtopics

Latent heat vs changes in u and h (don’t mix up properties)

Quality x and table use: u = u_f + x(u_g − u_f) (and analogous formulas)

Chemical and reactive systems (internal energy of reaction, formation energies)

Chapter 5

Measurement & data (how U is referenced, measured, and looked up)

Reference states and the “zero” of internal energy (why absolute U is arbitrary)

Calorimetry and experiments that determine ΔU and heat capacities

2 subtopics

Bomb calorimeter (constant-volume): interpret results as ΔU

Measure Cp/Cv (and note what DSC measures in practice)

Property tables and charts (steam tables, refrigerants, compressed liquid data)

Software/data sources for properties (when tables aren’t enough)

Estimating U from measurable properties (T, P, v, s) using identities

2 subtopics

Fundamental relation (simple compressible): du = T ds − P dv

Use Maxwell relations/identities to compute u(T,v) or u(T,P) when needed

Chapter 6

Problem solving & applications (using U in real analyses)

Energy-balance workflow: define system → write 1st law → apply models/tables

Closed-system problems (piston–cylinder, rigid tank, spring-loaded piston)

Control-volume problems (nozzles, throttles, turbines, compressors, mixers)

Cycles and performance calculations (where U changes show up)

2 subtopics

Air-standard Otto/Diesel/Brayton: track Δu across process steps

Refrigeration/heat-pump cycles: energy balances and where u/h are used

Common pitfalls & checks (signs, reference states, missing work terms)