A box contains two balls that can be either blue or red. A blue ball has an energy -E1 while a red ball has an energy E1. The box is connected to a heat bath of temperature T. a. Enumerate all the possible microstates and their corresponding energies. b. Calculate the partition function then write down the Helmholtz free energy. c. What is the probability that the box contains two red balls?
A box contains two balls that can be either blue or red. A blue ball has an energy -E1 while a red ball has an energy E1. The box is connected to a heat bath of temperature T. a. Enumerate all the possible microstates and their corresponding energies. b. Calculate the partition function then write down the Helmholtz free energy. c. What is the probability that the box contains two red balls?
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Transcribed Image Text:A box contains two balls that can be either blue or red. A
blue ball has an energy -E1 while a red ball has an energy
E1. The box is connected to a heat bath of temperature T.
a. Enumerate all the possible microstates and their
corresponding energies.
b. Calculate the partition function then write down the
Helmholtz free energy.
c. What is the probability that the box contains two red
balls?
d. Calculate the mean energy.
e. Solve for the entropy of the system.
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