Thermodynamics: Building Blocks

Problem :

Suppose we have a system of 3 particles, each of which can be in one of three states, A , B , and C , with equal probability. Write an expression that represents all of the possible configurations of the entire system, and determine which configuration will be most likely (such as "2 particles in state A , one in state B ").

Problem :

Return to the binary system discussed before. If the system consists of 5 particles, how many states of the entire system have 3 magnets in the up position?

Solution for Problem 2 >>

Here, we only need to plug in N = 5 and U = 3 into our equation for g(N, U) .

g(5, 3) = = 10

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Problem :

Take a system with 20 possible states, all equally likely. What is the probability of being in any particular state?

Problem :

In certain quantum scenarios, there are two distinct energy levels that a particle may occupy. Let one of the levels have an energy U which is equal to U ₁ = σ , and let the other level have energy U ₂ = 2 σ . Let us further suppose that the particle is twice as likely to be in level 1 than in level 2. What is the average value of the energy?

Solution for Problem 4 >>

We need to use the equation for average value of a property:

< U > = U(s)P(s) = σ + 2 σ = σ

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Problem :

State the Fundamental Assumption, and explain how it is related to the function P(s) .