Know what happens to an object if the rate at which it receives energy is less or more than the rate at which it transfers energy away from the object

2.3.3 Radiation

Objective

Understand what happens to an object when the rate at which it receives energy is less or more than the rate at which it transfers energy away from the object. ☀️❄️

Radiation Basics

Radiation is the transfer of energy by electromagnetic waves. It can happen in a vacuum, so it is the only way heat can travel in space. Every object emits radiation that depends on its temperature and surface properties.

Energy Balance

For an object in a steady state, the power it absorbs (\$P{\text{absorbed}}\$) equals the power it emits (\$P{\text{emitted}}\$). The net power is:



\$P{\text{net}} = P{\text{absorbed}} - P_{\text{emitted}}\$


If \$P{\text{net}} > 0\$, the object heats up. If \$P{\text{net}} < 0\$, it cools down. Think of a bathtub: the faucet is the energy source, the drain is the energy loss. If the faucet runs faster than the drain, the water level rises (the object warms). If the drain runs faster, the water level falls (the object cools). 🛁

Stefan‑Boltzmann Law

The power radiated by a black body is proportional to the fourth power of its absolute temperature:



\$P = \sigma A T^4\$


where:

  • \$\sigma = 5.67 \times 10^{-8}\,\text{W m}^{-2}\text{K}^{-4}\$ (Stefan‑Boltzmann constant)
  • \$A\$ is the surface area
  • \$T\$ is the temperature in Kelvin

Real objects have an emissivity \$\varepsilon\$ (0 < \$\varepsilon\$ ≤ 1) so:



\$P_{\text{emitted}} = \varepsilon \sigma A T^4\$


The absorbed power depends on the absorptivity \$\alpha\$ and the incident radiation \$I\$:



\$P_{\text{absorbed}} = \alpha I A\$


In many exam questions you’ll need to compare these two to decide if an object will warm or cool.

Examples & Analogies

  • ☀️ Earth in space – receives solar radiation, emits infrared. If the absorbed solar power > emitted power, the planet warms.
  • 🔥 Pot on a stove – the stove heats the pot; the pot radiates heat to the air. If the stove’s power > pot’s radiated power, the pot’s temperature rises.
  • ❄️ Ice cube in a room – the room’s infrared radiation is absorbed; the ice emits infrared. If absorbed power < emitted power, the ice melts.
  • 📚 Human body – we emit infrared radiation; if the environment is cooler, we lose heat and feel cold.
  • 🚀 Satellite in orbit – no air, so only radiation balances the heat from solar panels and internal electronics.

Radiation Types Table

Wavelength RangeCommon NameTypical Energy
> 700 nmInfraredLow (thermal)
400–700 nmVisibleModerate
10–400 nmUltravioletHigh (can damage)

Sample Calculation

A black body (ε = 1) with area 0.5 m² is at 300 K.



\$P_{\text{emitted}} = \sigma A T^4 = (5.67\times10^{-8})(0.5)(300)^4 \approx 1.5\times10^{2}\,\text{W}\$


If it receives 200 W of solar radiation (α = 1), the net power is 200 W – 150 W = 50 W, so the body will warm up.


If it receives only 100 W, the net power is –50 W, so it will cool down.

Exam Tips

  • Always check if the object is in radiative equilibrium (Pabsorbed = Pemitted).
  • Use the Stefan‑Boltzmann law for radiative power: \$P = \varepsilon \sigma A T^4\$.
  • Remember that absorptivity = emissivity for a given material at a given wavelength.
  • When a question gives only temperature and area, you can calculate emitted power directly.
  • Check units carefully – power is in watts (W), temperature in kelvin (K), area in square metres (m²).
  • Use the bathtub analogy to explain net heating or cooling.
  • For multiple surfaces, sum the powers from each surface.