Understand what happens to an object when the rate at which it receives energy is less than, equal to, or greater than the rate at which it transfers energy away.
Key Concepts
All objects emit electromagnetic radiation according to their temperature.
The net energy change of an object depends on the balance between energy received and energy lost.
If the net energy gain is positive, the object's temperature rises; if negative, the temperature falls; if zero, the object is in thermal equilibrium.
Energy Transfer by Radiation
The power radiated by a surface is given by the Stefan‑Boltzmann law:
\$P{\text{rad}} = \sigma A e \left(T^{4} - T{\text{env}}^{4}\right)\$
where:
\(\sigma = 5.67 \times 10^{-8}\ \text{W m}^{-2}\text{K}^{-4}\) is the Stefan‑Boltzmann constant,
\(A\) is the surface area of the object,
\(e\) is the emissivity (0 ≤ e ≤ 1),
\(T\) is the absolute temperature of the object (K),
\(T_{\text{env}}\) is the absolute temperature of the surroundings (K).
Energy Balance Scenarios
Scenario
Energy Received (\(P_{\text{in}}\))
Energy Lost (\(P_{\text{out}}\))
Net Power (\(P{\text{net}} = P{\text{in}}-P_{\text{out}}\))
Resulting Behaviour
1. \(P{\text{in}} < P{\text{out}}\)
Less than the power radiated away
Greater than the power received
Negative
Object cools – temperature falls until equilibrium is reached.
2. \(P{\text{in}} = P{\text{out}}\)
Exactly equal to the power radiated away
Exactly equal to the power received
Zero
Thermal equilibrium – temperature remains constant.
3. \(P{\text{in}} > P{\text{out}}\)
Greater than the power radiated away
Less than the power received
Positive
Object heats – temperature rises until a new equilibrium is achieved.
Practical Examples
Sun‑lit surface: A black asphalt road receives solar radiation (\(P_{\text{in}}\)) that exceeds its radiative loss at night, so its temperature rises during the day.
Radiator in a cold room: The radiator emits more heat than it receives from the room, giving \(P{\text{out}} > P{\text{in}}\); the room temperature gradually increases until equilibrium.
Spacecraft thermal control: Surfaces are coated to adjust emissivity so that \(P{\text{in}}\) (solar + internal) matches \(P{\text{out}}\), maintaining a stable internal temperature.
Factors Influencing Energy Transfer
Emissivity (e): Dark, matte surfaces have high emissivity and lose energy quickly; shiny, reflective surfaces have low emissivity and retain heat.
Surface Area (A): Larger area increases both received and emitted power proportionally.
Temperature difference: Because radiated power depends on \(T^{4}\), small changes in temperature cause large changes in emitted power.
Surrounding temperature (\(T_{\text{env}}\)): A hotter environment reduces net loss, possibly turning it into a net gain.
Summary
Whether an object heats up, cools down, or stays at a constant temperature depends on the sign of the net power:
Net gain (\(P_{\text{net}} > 0\)) → temperature rises.
Net loss (\(P_{\text{net}} < 0\)) → temperature falls.
Net zero (\(P_{\text{net}} = 0\)) → thermal equilibrium.
Suggested diagram: Energy flow diagram showing incoming solar radiation, emitted infrared radiation, and the balance that determines heating, cooling, or equilibrium.