On March 20, 1879, 44-year-old Slovenian-Austrian physicist Josef Stefan (1835–1893) presented his landmark paper to the Imperial Academy of Sciences in Vienna titled “Über die Beziehung zwischen der Wärmestrahlung und der Temperatur”.

Stefan empirically discovered Stefan’s Law, proving that the total radiant power per unit surface area emitted by a blackbody is directly proportional to the fourth power of its absolute thermodynamic temperature ($T^4$).

Empirical Derivation & Stefan-Boltzmann Constant ($\sigma$)

Stefan analyzed experimental cooling data collected by John Tyndall on glowing platinum wires ($525^\circ\text{C}$ to $1200^\circ\text{C}$):

1. The $T^4$ Power Law

Stefan discovered that the ratio of total radiant energy emitted at $1473\,\text{K}$ ($1200^\circ\text{C}$) compared to $798\,\text{K}$ ($525^\circ\text{C}$) was $(1473/798)^4 \approx 11.6$, matching Tyndall’s measured heat emission ratio.

2. The Stefan-Boltzmann Formula

For a blackbody of surface area $A$ at absolute temperature $T$:

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

Where $\sigma$ is the Stefan-Boltzmann Constant:

$$\sigma = \frac{2\pi^5 k_{\text{B}}^4}{15 c^2 h^3} \approx 5.670374 \times 10^{-8}\,\text{W}\cdot\text{m}^{-2}\cdot\text{K}^{-4}$$

3. Theoretical Proof by Boltzmann (1884)

In 1884, Stefan’s student Ludwig Boltzmann derived the $T^4$ law theoretically from Maxwell’s radiation pressure ($P = u/3$) and the Second Law of Thermodynamics ($\text{Stefan-Boltzmann Law}$).

Solar Temperature Calculation

Using his $T^4$ law and Langley’s solar flux data, Stefan made the world’s first accurate calculation of the Sun’s surface temperature ($T_{\text{Sun}} \approx 5,700\,\text{K}$).

Key Takeaways

  • Year: 1879
  • Key Figure: Josef Stefan (Slovenian-Austrian Physicist)
  • Core Discovery: Discovered Stefan’s Law ($P = \sigma T^4$), proving total blackbody radiation scales as $T^4$.
  • Solar Physics: First accurate calculation of the Sun’s surface temperature ($5,700\,\text{K}$).
  • Quantum Relevance: Integrates Max Planck’s quantum distribution over all frequencies ($\int_0^\infty u(\nu) d\nu = \sigma T^4$).