A box contains two balls that can be either blue or red. A blue ball has an energy -E0 while a red ball has an energy E0. The box is connected to a heat bath of temperature T. i. Enumerate all the possible microstates and their corresponding energies. ii. Calculate the partition function then write down the Helmholtz free energy.  iii. What is the probability that the box contains two red balls?

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Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell established the context for the distribution of molecular velocities for random molecules moving in a closed environment. This theory was generalized in 1871 by German physicist Ludwig Boltzmann. He improvised the theory to express the distribution of energy levels among different molecules.