# Planck had 2 definitions of energy in 1900, how?

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• Cool4Kat
In summary, in 1900, Max Planck introduced two different definitions of energy, the classical definition and the quantum definition. The classical definition, based on the laws of thermodynamics, described energy as a continuous and linearly increasing quantity. However, Planck's quantum definition, based on his groundbreaking theory of quantum mechanics, described energy as being quantized into discrete packets or "quanta." This marked a significant shift in understanding energy and laid the foundation for modern physics.
Cool4Kat
TL;DR Summary
Planck's 1900 paper appears to have two equations for the energy, hf, and hf/(e^(hf/kT)-1), how does that work?
So, I was looking into Einstein's 1907 paper where he derived the specific heat of solids using quantum mechanics and I found that Einstein just took the derivative of Planck's equation from 1900 for the average energy, U, as a function of time (and multiplied it by 3N for the three dimensions). Anyway, that makes sense for Einstein but then I got very confused about Planck in 1900.

This is the same paper that Planck said that light was created in little energy elements with energy equal to hf. So, how can the average energy = hf/(e^(hf/kT)-1)? I feel like that means that the energy has two definitions. I feel like I am missing something basic, what is it?

Thank you so much!

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Cool4Kat said:
Summary: Planck's 1900 paper appears to have two equations for the energy, hf, and hf/(e^(hf/kT)-1), how does that work?

In Planck's proposal, there are many energy levels - the difference between each neighbouring pair of levels if hf.

When things are in equilibrium at temperature T, the probability with which the different energy levels are occupied is such that the average energy is hf/(e^(hf/kT)-1).

The derivation is given in http://galileo.phys.virginia.edu/classes/252/PlanckStory.htm.

dlgoff

## 1. What were Planck's two definitions of energy in 1900?

In 1900, Max Planck proposed two different definitions of energy: the classical definition and the quantum definition. The classical definition was based on the idea that energy could be continuously divided into smaller and smaller units, while the quantum definition stated that energy could only exist in discrete packets or quanta.

## 2. Why did Planck propose two definitions of energy?

Planck proposed the two definitions of energy in response to a problem with the classical theory of thermodynamics. The classical theory predicted that the energy of a blackbody should increase infinitely as the wavelength of light decreases, which was not observed in experiments. Planck's quantum definition of energy helped to resolve this issue.

## 3. How did Planck's quantum definition of energy differ from the classical definition?

The classical definition of energy stated that it could be continuously divided into smaller units, while the quantum definition proposed that energy could only exist in discrete packets or quanta. This meant that energy was not continuous and could only change in specific increments, rather than being able to take on any value.

## 4. Did Planck's two definitions of energy have any impact on the development of quantum mechanics?

Yes, Planck's two definitions of energy were crucial in the development of quantum mechanics. His quantum definition of energy laid the foundation for the concept of quantization, which became a fundamental principle in quantum mechanics. This led to the development of new theories and models that revolutionized our understanding of the behavior of particles at the atomic and subatomic level.

## 5. How do Planck's two definitions of energy relate to his famous equation, E=mc²?

Planck's two definitions of energy were important precursors to Einstein's famous equation, E=mc². The quantum definition of energy showed that energy and mass were fundamentally related, and this idea was further developed by Einstein in his theory of special relativity. This equation has had a significant impact on modern physics and has been confirmed through numerous experiments and observations.

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