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Consider a system of classical non-interacting particles constrained to be in the XY plane sub ject to the potential: V(x, y) = 1/2 * alpha * (x - y) ^ 2 If they are in equilibrium with a thermal bath at temperature T', what is the average energy per particle? The Boltzmann constant is k_{B}?
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Consider a system of classical non-interacting particles constrained t...


System Description:

The system consists of classical non-interacting particles confined to the XY plane and subject to the potential V(x, y) = 1/2 * alpha * (x - y) ^ 2.

Average Energy Calculation:

To determine the average energy per particle, we need to consider the Boltzmann distribution function. The average energy can be calculated using the formula:

E_avg = ∫ E * exp(-E/k_{B}T') / Z dE

where E represents the energy of a particle, k_{B} is the Boltzmann constant, T' is the temperature of the thermal bath, and Z is the partition function.

Partition Function Calculation:

The partition function Z can be calculated as:

Z = ∫ exp(-E/k_{B}T') dE

For the given potential V(x, y) = 1/2 * alpha * (x - y) ^ 2, the energy E can be expressed as E = 1/2 * alpha * (x - y) ^ 2.

Integration:

Substitute E into the partition function equation and perform the integration to obtain the partition function Z.

Average Energy:

Once the partition function Z is determined, substitute it into the average energy formula to calculate the average energy per particle of the system.

Final Result:

The final result will provide the average energy per particle of the system in equilibrium with the thermal bath at temperature T'.
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Consider a system of classical non-interacting particles constrained to be in the XY plane sub ject to the potential: V(x, y) = 1/2 * alpha * (x - y) ^ 2 If they are in equilibrium with a thermal bath at temperature T', what is the average energy per particle? The Boltzmann constant is k_{B}?
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Consider a system of classical non-interacting particles constrained to be in the XY plane sub ject to the potential: V(x, y) = 1/2 * alpha * (x - y) ^ 2 If they are in equilibrium with a thermal bath at temperature T', what is the average energy per particle? The Boltzmann constant is k_{B}? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider a system of classical non-interacting particles constrained to be in the XY plane sub ject to the potential: V(x, y) = 1/2 * alpha * (x - y) ^ 2 If they are in equilibrium with a thermal bath at temperature T', what is the average energy per particle? The Boltzmann constant is k_{B}? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a system of classical non-interacting particles constrained to be in the XY plane sub ject to the potential: V(x, y) = 1/2 * alpha * (x - y) ^ 2 If they are in equilibrium with a thermal bath at temperature T', what is the average energy per particle? The Boltzmann constant is k_{B}?.
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