The Boltzmann Law Describes Equilibria

The Boltzmann Distribution Law Describes the Equilibria Among Atoms and Molecules 

Consider a system having N particles. (To make the math simple in this chapter, consider N particles of a single type, rather than a set of N =. .., Nm) 

Differentiating with respect to pj (holding the p, s constant) gives 

To get dU, we postulate that the internal energy U, which is the macroscopic-quantity from thermod mamics, is the average over the microscopic energy- 

The First Law gives dU = 6q + 6w, which reduces to d E) = dU = Sq when V and N are constant. Because Equation (10.4) applies when V is constant, it follows that the term. j Ejdpj is the heat, and Xj PjdEj is the work. 

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