Exploring the Concept of Zero Chemical Potential in Photons: A Clear Explanation

In summary, photons have zero chemical potential because their energy is directly proportional to the number of photons of given frequency.
  • #1
efaizi
12
0
Hi
Why photon has zero chemical potential. please answer this question clearly.
 
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  • #2
The energy of photons is directly proportional to the number of photons of given frequency, hence we cannot specify energy and particle number independently. beta=1/kT and mu are the conjugated variables corresponding to energy and particle number respectively. Hence only one of the two is sufficient to specify the system. Instead of setting mu=0 it would be either possible to set beta=0.
 
  • #3
The previous answer may be more rigorous, but this here is my way to understand it. Since the number of photons can fluctuate freely, the average number of photons is obtained by minimizing the free energy with respect to N, i.e. by setting dF/dN=0. But by statistical mechanics, dF/dN at constant T and V is equal to the chemical potential.
 
  • #4
Does this have implications in the production of photons? I seem to recall reading somewhere that the chemical potential is the energy required to create the particle excluding rest mass, so the photon with zero rest mass and zero chemical potential carries all the energy of its formation?
 
  • #5
There is two problem: first is what is freely photon fluctation? The second is : Do the other particles follow the minimum free energy? is yes, then they have also zero chemical potentials!
 
  • #6
Other particles have conservation laws the keep the chemical potential from going to zero. For example electrons cannot be created or destroyed "at will" in order to minimize the free energy because that would violate conservation of charge (and lepton number, angular momentum, etc.)
 
  • #7
One thing you may want to note about is that the chemical potential of the bosonic particles in BEC is zero. What can it mean except to avoid having negative Bose-Einstein distribution function?
 
  • #8
only in the non-interacting BEC case, the chemical potential is zero. And here it indicates that particle number in the the ground state can change, or to put it another way, the ground state is a particle bath.
 
  • #9
I think that is because photon is gapless, which means you can creat or kill one very easy. While the chemical potential is a parameter which describe "how difficult" you put one particle into your system. In this way, all particles(including quasi-particles) with zero mass will have zero chemical potential.
 

What is zero chemical potential?

Zero chemical potential is a thermodynamic concept that refers to the state in which there is no net transfer of particles between two systems that are in thermal equilibrium. It is the point at which the chemical potential of a substance is equal to zero, indicating that the system is in equilibrium and there is no driving force for particles to move from one system to another.

How is zero chemical potential related to temperature?

Zero chemical potential is directly related to temperature through the Gibbs-Duhem equation, which states that at constant pressure and temperature, the chemical potential of a substance is equal to the molar enthalpy divided by the temperature. This means that as the temperature increases, the chemical potential also increases, and at zero chemical potential, the temperature is at its maximum value.

What does zero chemical potential indicate about a system?

Zero chemical potential indicates that a system is in equilibrium and there is no driving force for particles to move between two systems. This means that the system is at a stable state and will remain at this state unless external factors, such as changes in temperature or pressure, are introduced.

Can the chemical potential of a substance be negative?

Yes, the chemical potential of a substance can be negative. This occurs when there is a driving force for particles to move from one system to another, as the chemical potential is a measure of the energy required for this transfer to take place. A negative chemical potential indicates that the particles will move from the system with a lower chemical potential to the one with a higher chemical potential.

What is the significance of zero chemical potential in chemistry?

Zero chemical potential is significant in chemistry as it indicates the point of equilibrium between two systems. It is a useful concept in understanding and predicting the behavior of chemical systems, as well as in determining the conditions necessary for reactions to occur. It also has practical applications in fields such as thermodynamics, electrochemistry, and material science.

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