Physics for ME · Chapter 11 of 16 · Intermediate
Thermal Physics: Temperature, Heat, and Material Response
Materials expand, store heat, and change phase. This chapter is the bridge to Thermodynamics, Heat Transfer, and Materials Science.
Readiness check
From Chapters 1 and 6. Tick only what you can do closed-notes.
- Keep joules, watts, and degrees distinct.
- Work with 10⁻⁶-scale coefficients without slips.
- Run an energy audit with named accounts (Chapter 6).
- Convert Celsius and kelvin, knowing when each matters.
- Read a simple material-property table.
The core idea
Temperature measures molecular agitation; heat is energy in transit; materials respond by expanding, storing, or transforming.
ΔL = αLΔTQ = mcΔTQ = mLfThree material responses cover most engineering: expansion (α), sensible heating (c), and phase change (latent heat). Heat moves by conduction, convection, and radiation: named here, quantified in the Heat Transfer course.
What this chapter covers
- 11.1 Temperature and thermometers: Celsius, kelvin, and thermal equilibrium.
- 11.2 Thermal expansion: linear, area, and volume; blocked expansion as stress.
- 11.3 Heat and heat capacity: Q = mcΔT and material differences.
- 11.4 Phase changes: latent heat, melting, boiling.
- 11.5 Kinetic theory glimpse: temperature as molecular kinetic energy.
- 11.6 Heat transfer modes: conduction, convection, radiation, by name and intuition.
Engineering connection: the bridge to Thermodynamics, Heat Transfer, and Materials. OpenStax Vol. 2 opens here.
Worked example: the rail gap
A 30 m steel rail (α = 12 × 10⁻⁶ /K) is laid at 15 °C and can reach 55 °C in summer. What expansion gap must the track design allow, and what happens if the rail is fully clamped instead?
- ProblemSize the expansion gap in Figure 1 and assess the clamped case.
- Given / findL = 30 m, α = 12 × 10⁻⁶ /K, ΔT = 40 K. Find ΔL; then the clamped-rail stress.
- AssumptionsUniform temperature, constant α over the range, free expansion in the first case.
- ModelLinear expansion for the gap; for the clamped rail, the suppressed strain αΔT becomes elastic stress σ = EαΔT (preview of Mechanics of Materials, E = 200 GPa for steel).
- EquationsΔL = αLΔT σ = EαΔT (if blocked)
- SolveΔL = 12 × 10⁻⁶ × 30 × 40 = 1.44 × 10⁻² m = 14.4 mm. Clamped: σ = 200 × 10⁹ × 12 × 10⁻⁶ × 40 = 96 MPa of compression.
- CheckUnits: /K × m × K = m. Scale: millimetres on a 30 m rail (about 0.05%) is the right order for metals. The 96 MPa is near half of mild steel's yield: severe, as the buckled-track photos in any railway handbook confirm.
- ConclusionGive the rail its 14.4 mm or it will take 96 MPa instead: expansion either moves or loads, never disappears. Every bridge roller, pipeline loop, and engine clearance traces back to this trade.
Misconceptions and diagnostics
| Mistake | Symptom | Diagnostic question | Correction |
|---|---|---|---|
| Heat and temperature interchanged | "The oven has lots of temperature" | "Amount of energy, or level of agitation?" | Heat is energy in transit (J); temperature is the level (K). A sparkler is hot, a bathtub holds more heat. |
| Celsius in ratio formulas | Gas-law and radiation answers nonsensical | "Does this formula compare absolute levels?" | Differences may use °C; ratios and gas laws demand kelvin. |
| Phase change expected to warm | Melting ice "should" rise above 0 °C | "Where is the energy going during the change?" | Into breaking bonds: temperature holds while Q = mL is paid. |
| Holes expected to shrink on heating | Shrink-fit logic inverted | "Does the hole behave like the missing disc?" | Holes expand like the material that would fill them: that is why heated bearings slip onto shafts. |
Practice ladder
How much energy heats 2.0 kg of aluminium (c = 900 J/kg·K) from 20 °C to 70 °C?
Show answer
Q = 2 × 900 × 50 = 90 kJ.
A 3 kW kettle holds 1.5 kg of water at 20 °C (c = 4186 J/kg·K). How long to reach 100 °C, and how much longer to boil 0.2 kg away (Lv = 2.26 MJ/kg)?
Show answer
Heating: Q = 1.5 × 4186 × 80 = 502 kJ, t = 502/3 = 167 s. Boiling 0.2 kg: Q = 452 kJ, another 151 s. The latent step nearly matches the entire 80-degree climb: phase change is expensive.
A steel shaft of 80.000 mm must enter a bearing bored to 79.940 mm by cooling the shaft (α = 12 × 10⁻⁶ /K). What temperature drop is needed for 0.02 mm of working clearance?
Show answer
Required shrink = 0.060 + 0.020 = 0.080 mm. ΔT = ΔL/(αL) = 0.08/(12 × 10⁻⁶ × 80) = 83 K: cool to about −63 °C, a dry-ice or nitrogen job. The same arithmetic runs every shrink-fit drawing.
Find one real expansion provision (bridge joint, pipeline loop, slotted screw hole on a fence rail) and one real shrink/interference fit. Estimate the ΔL each must handle from sizes and a plausible ΔT.
What good work looks like
Photos or sketches, the αLΔT estimate for each with a stated α, and a comparison of the provision's travel against the computed need.
Working with AI, and proving it yourself
Use AI as an examiner, not a solver
Portfolio task
Measure water's heat capacity with a kettle: known power, known mass, timed temperature rise. Compare your c with 4186 J/kg·K and account for the losses that explain your (inevitable) overshoot of the true value.
Retrieval and spaced review
Closed notes. Answer out loud, then reveal.
1. Distinguish heat, temperature, and internal energy.
Temperature: the agitation level (K). Internal energy: the stored molecular energy (J). Heat: energy moving between bodies because of a temperature difference (J).
2. Write the three material-response equations.
ΔL = αLΔT; Q = mcΔT; Q = mL (latent, at constant temperature).
3. What happens when thermal expansion is prevented?
The suppressed strain becomes stress: σ = EαΔT, often structurally serious (96 MPa in the rail example).
4. Name the three heat-transfer modes with one example each.
Conduction (handle of a pan), convection (radiator warming a room), radiation (sun, glowing heater). Quantified in Heat Transfer.
5. Why must gas laws use kelvin?
They relate ratios to absolute molecular energy; Celsius has an arbitrary zero and breaks the proportionality.
Textbook mapping
| Item | Mapping |
|---|---|
| Main source | OpenStax University Physics Vol. 2, Temperature and Heat (opening chapters) |
| Reference | Young and Freedman · Halliday, Resnick and Walker |
| Core topics | 11.1 Temperature · 11.2 Expansion · 11.3 Heat capacity · 11.4 Phase change · 11.5 Kinetic theory glimpse · 11.6 Transfer modes by name |
| Engineering connection | Bridge to Thermodynamics, Heat Transfer, and Materials Science; thermal stress previews Mechanics of Materials. |
| Read next | Chapter 12: First Law of Thermodynamics and Energy Balance. |