The Stefan-Boltzmann Law
The amount of radiation an object emits is directly proportional to the fourth power of its absolute temperature. This is described by the Stefan-Boltzmann Law:
* P = σ * A * T⁴
Where:
* P is the power radiated (energy per unit time)
* σ is the Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²K⁴)
* A is the surface area of the object
* T is the absolute temperature in Kelvin
Calculating the Difference
Let's calculate the ratio of radiation emitted by the two objects:
* P₁ / P₂ = (σ * A * T₁⁴) / (σ * A * T₂⁴)
* P₁ / P₂ = (T₁⁴) / (T₂⁴)
* P₁ / P₂ = (1000 K)⁴ / (1200 K)⁴ ≈ 0.48
This means the object at 1000 K emits roughly half the radiation of the object at 1200 K.
Key Point: Even a small change in temperature leads to a substantial change in the amount of radiation emitted due to the fourth power relationship.
