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aaaa202

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One would assume that if the energy is high there'd be a greater tendency to be in excited states or am I wrong?

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- Thread starter aaaa202
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In summary, the Boltzmann distribution for a collection of atoms is independent of their total energy because it depends only on their temperature. This is due to the fact that in a closed system in thermal equilibrium, energy is conserved on average and the total energy is fixed by the temperature. This creates a one-to-one correspondence between the average energy and temperature. However, in certain cases, such as for an ideal monatomic gas, the ground state may still be more probable even if the energy of the system is much larger than the energy of the ground state. This is because temperature is not directly equivalent to energy and can still remain constant even with a large energy value.

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aaaa202

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One would assume that if the energy is high there'd be a greater tendency to be in excited states or am I wrong?

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[tex]U=\langle E \rangle=\frac{3}{2} N k T,[/tex]

where [itex]T[/itex] is the absolute temperature, [itex]N[/itex] the particle number contained in the subsystem, and [itex]k[/itex] Boltzmann's constant.

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aaaa202

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If you try to find the probability of an atom in hot resevoir of other atoms appearing in an excited state at T=300K you find that the probability of finding the atom in the ground state is overwhelmingly more probable.

But what if the energy of the system of N particles is so big, that E/N is far larger than the energy of the ground state. How can the ground state then still be so probable? We still assume that T=300K (temperature isn't directly the same as energy, so isn't this possible?)

The Boltzmann distribution is a statistical probability distribution that describes the distribution of energy among particles in a system at a specific temperature. It is used to understand the behavior of thermodynamic systems and can be applied to a wide range of systems, from gases to solid materials.

The Boltzmann distribution is based on the principles of thermodynamics, which state that energy flows from hotter objects to colder objects until they reach thermal equilibrium. Therefore, the temperature of a system determines the average energy of its particles and the distribution of that energy.

As the temperature of a system increases, the average energy of its particles also increases. This leads to a wider distribution of energies among the particles, resulting in a flatter Boltzmann distribution curve. Conversely, as the temperature decreases, the distribution curve becomes narrower and taller.

Aside from temperature, the Boltzmann distribution can also be influenced by external factors such as pressure, volume, and the type of particles in the system. However, these factors have a smaller impact compared to temperature, which remains the primary determinant of the distribution.

The Boltzmann distribution is widely used in various fields, including physics, chemistry, and engineering. It is used to predict the behavior of gases, study molecular dynamics, and understand the properties of materials. It also plays a crucial role in the development of technologies such as thermoelectric devices, solar cells, and refrigeration systems.

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