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 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.
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). 🛁
The power radiated by a black body is proportional to the fourth power of its absolute temperature:
\$P = \sigma A T^4\$
where:
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.
| Wavelength Range | Common Name | Typical Energy |
|---|---|---|
| > 700 nm | Infrared | Low (thermal) |
| 400–700 nm | Visible | Moderate |
| 10–400 nm | Ultraviolet | High (can damage) |
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.