Thermal radiation
Nothing movesA hot body radiating to a sensor: the fourth power of the temperature, the inverse square of the distance, and the colour it glows.
Gases & thermodynamics — Pressure, volume and temperature, and the particles whose motion they average.
Experiments already set up on it
The fourth power
The headline: ln P against ln T is straight, with a gradient of four.
- P = εσAT⁴
- So ln P against ln T is straight with a gradient of exactly 4
- A log–log graph is how you measure a power law you do not already know
The inverse square law
Move the sensor away: the intensity falls as 1/d².
- The same power spreads over a sphere, whose area goes as d²
- So I against 1/d² is a straight line through the origin
- Nothing is absorbed on the way — the spreading is the whole effect
Does the surface matter?
Same temperature, same size: a shiny surface radiates a fraction as much.
- ε multiplies everything, and it is a property of the surface
- A good emitter is a good absorber, which is why a radiator is painted
- And why a thermos flask is silvered inside
What colour is it?
Wien’s law: the hotter it gets, the shorter the wavelength it peaks at.
- λ_max = b/T, so λ_max against 1/T is straight
- Which is why a poker goes dull red, then orange, then white
- And why the Sun at 5800 K peaks in the middle of what we can see
What you can measure
Each of these can be recorded over time, aggregated over a run, or read at the moment something happens — through an instrument that carries its own uncertainty.
- Power radiatedP (W)
- Net power lostP_n (W)
- Intensity at the sensorI (W/m^2)
- 1/d²invd2 (1/m^2)
- TemperatureT (K)
- Surface areaA (m^2)
- Emissivityε
- Wavelength it is brightest atλmax (nm)
What you can change
Any of these can be the thing you vary, and every combination of the ones you choose is run as its own trial.
- TemperatureT (K)
- Radius of the spherer (cm)
- Temperature of the roomT₀ (K)
- Distance to the sensord (m)
The equations behind it
What thermal radiation is built on. Every one of these is in the lab's formula reference too, where it copies straight into a write-up.
Thermal energy transfers
- Heating something up — c is the specific heat capacity.
- Changing state — L is the specific latent heat; the temperature does not change.
- Density
- Kelvin from Celsius
Energy radiated
- Stefan–Boltzmann law — For a black body; multiply by the emissivity otherwise.
- Wien’s displacement law — λ in metres, T in kelvin.
- Intensity at a distance
- Albedo
Also in Gases & thermodynamics
Ideal gases
Squeeze, heat and cool a box of atoms. The pressure is measured from the hammering on the walls and the temperature from how fast they are going.
Heating and cooling
Heat a measured mass with a known power and watch the temperature. The plateaus are where the energy is going into melting or boiling instead.
Heat engines
Take a gas round a closed cycle and measure the area of the loop. How much of the heat you pay for comes back as work — and why can none of them do better than Carnot?