Hubungan Rumus Pergeseran Wien dengan Hukum Planck dan Hukum Stefan-Boltzmann
The study of blackbody radiation, the electromagnetic radiation emitted by an idealized object that absorbs all incident radiation, has been instrumental in shaping our understanding of quantum mechanics and the nature of light. This phenomenon is governed by fundamental laws, including Planck's law, Stefan-Boltzmann law, and Wien's displacement law, which are interconnected and provide a comprehensive framework for analyzing the spectral distribution of blackbody radiation. This article delves into the intricate relationship between Wien's displacement law and the other two laws, exploring their theoretical underpinnings and practical implications.
Wien's Displacement Law and Its Significance
Wien's displacement law, formulated by Wilhelm Wien in 1893, establishes a relationship between the wavelength at which a blackbody emits the maximum radiation and its temperature. It states that the product of the wavelength of maximum emission (λmax) and the temperature (T) is a constant, known as Wien's displacement constant (b). Mathematically, this can be expressed as:
λmax * T = b
This law has profound implications for understanding the spectral distribution of blackbody radiation. It explains why hotter objects emit radiation at shorter wavelengths, resulting in a shift towards the blue end of the spectrum. Conversely, cooler objects emit radiation at longer wavelengths, appearing redder. This phenomenon is readily observed in everyday life, from the glowing embers of a fire to the faint red glow of a distant star.
Connecting Wien's Law to Planck's Law
Planck's law, derived by Max Planck in 1900, provides a more comprehensive description of the spectral distribution of blackbody radiation. It states that the spectral radiance of a blackbody at a given wavelength and temperature is proportional to the Planck function, which is a function of wavelength and temperature. Planck's law can be expressed as:
B(λ, T) = (2hc²/λ⁵) * (1/(e^(hc/λkT) - 1))
where h is Planck's constant, c is the speed of light, and k is Boltzmann's constant.
Wien's displacement law can be derived from Planck's law by finding the wavelength at which the Planck function reaches its maximum value. This involves differentiating the Planck function with respect to wavelength and setting the derivative equal to zero. Solving this equation leads to the expression for Wien's displacement law. Therefore, Wien's law can be seen as a special case of Planck's law, specifically focusing on the wavelength of maximum emission.
The Role of Stefan-Boltzmann Law
The Stefan-Boltzmann law, formulated by Josef Stefan in 1879 and later derived by Ludwig Boltzmann in 1884, relates the total energy radiated per unit area of a blackbody to its temperature. It states that the total energy radiated per unit area (E) is proportional to the fourth power of the absolute temperature (T):
E = σT⁴
where σ is the Stefan-Boltzmann constant.
While Wien's displacement law focuses on the wavelength of maximum emission, the Stefan-Boltzmann law provides information about the total energy radiated by a blackbody. The two laws are complementary, providing a complete picture of the spectral distribution and total energy emitted by a blackbody.
Conclusion
The relationship between Wien's displacement law, Planck's law, and Stefan-Boltzmann law is fundamental to understanding blackbody radiation. Wien's law, derived from Planck's law, provides a specific relationship between the wavelength of maximum emission and temperature. The Stefan-Boltzmann law, on the other hand, quantifies the total energy radiated by a blackbody. Together, these laws offer a comprehensive framework for analyzing the spectral distribution and energy output of blackbody radiation, which has significant implications in various fields, including astrophysics, thermal engineering, and materials science.