Thermal Physics: quick revision, 13 bites

The Perfect Absorber

Black bodies absorb everything.

A **black body** is an idealized object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It reflects nothing.

Takeaway. A black body is a perfect absorber, not necessarily black in color.

Cavity Radiator Model

A hole in a box.

The best practical approximation of a black body is a **cavity radiator**: a hollow metal box with a tiny hole. Radiation entering the hole undergoes multiple reflections and is almost completely absorbed.

Takeaway. A small hole in a cavity acts as a near-perfect black body.

Kirchhoff's Law

Good absorbers are good emitters.

**Kirchhoff's law of thermal radiation** states that at thermal equilibrium, the emissivity of a body equals its absorptivity at a given wavelength and temperature: $e_\lambda = a_\lambda$.

Takeaway. A perfect absorber is also a perfect emitter.

Stefan-Boltzmann Law

Power scales with T to the fourth.

This law gives the total power radiated across all wavelengths. Doubling temperature increases radiated power by $2^4 = 16$ times.

Takeaway. Total radiated power is proportional to the fourth power of absolute temperature.

Wien's Displacement Law

Hotter bodies glow bluer.

As temperature increases, the peak wavelength shifts to **shorter wavelengths** (higher frequencies). This explains why heated objects first glow red, then yellow, then white.

Takeaway. Peak wavelength is inversely proportional to temperature.

Black Body vs Real Body

Ideal vs actual emitters.

Takeaway. Real bodies are grey or selective emitters, never perfect black bodies.

Sun as a Black Body

Our star approximates a black body.

The Sun's spectrum closely resembles a black body curve at about **5800 K**. Its peak wavelength is in the visible range (green-blue), which is why our eyes evolved to see this region.

Takeaway. The Sun is a near-perfect black body at 5800 K.

Earth's Energy Balance

Our planet radiates infrared.

Earth absorbs solar radiation (mostly visible) and re-emits it as **infrared radiation** (around 255 K). This balance determines our climate.

Takeaway. Black body radiation governs planetary temperatures.

Black Body Isn't Always Black

Color is misleading.

A black-painted surface is a good absorber in visible light but may not be a perfect black body across all wavelengths.

Takeaway. Black body means perfect absorber, not visually black.

Spectral Distribution

Intensity vs wavelength curves.

Takeaway. The black body spectrum is a universal curve shape that shifts with temperature.

Pyrometry

Measuring temperature remotely.

**Optical pyrometers** measure the radiation from a hot object to determine its temperature without contact. Used in furnaces, molten metals, and stars.

Takeaway. Non-contact temperature measurement uses black body radiation.

Cosmic Microwave Background

The universe is a black body.

The **Cosmic Microwave Background (CMB)** radiation is the most perfect black body spectrum ever observed, at a temperature of **2.725 K**. It is remnant radiation from the early universe.

Takeaway. The CMB is the best natural black body spectrum known.

Remember the Constants

Don't mix up b and σ.

Takeaway. Memorize b and σ with their units.