Find the probability distribution for the energy of a, Mechanical Engineering

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Find the probability distribution for the energy of a

Relativistic particles in a gravitational field

Consider N relativistic ideal-gas particles at temperature T. The particles are confined to a three-dimensional box of area A and 0

1. Find the probability distribution for the height of a single particle, i.e.: P(z₁).

2. Find the average height of a single particle.

3. In what way did your answer for the average height depend on the relativistic nature of the particles?

4. Find the probability distribution for the energy of a single particle, E₁ = |p₁|c + mgz1, including the normalization constant.

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Mechanical Engineering: Find the probability distribution for the energy of a

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