Question 4: The Ensemble of Pressures: Imagine that you bring a system into contact with a reservoir of heat and work (or Thermal and volume reservoirs). The wall connecting the system and the reservoir is diathermal and can also move. a) Using the same formalism used to find the Boltzmann factor (Chapter 3) and the Gibbs factor (Chapter 5), derive in detail an expression for the equivalent factor related to the reservoir in question. We can baptize this factor as âPressure factorâ. b) Find the partition function for the problem. c) Find expressions for U (average internal energy) and <V> (average volume).
Consider a small system that is interacting with a reservoir at temperature 400 K, pressure 108 Pa, and chemical potential ‒0.3 eV.
(a) To go from state 1 to state 2, the small system must take an additional 0.03 eV of energy and 10‒29 m3 of volume from the reservoir. How many times more probable is it for the small system to be in state 1 than state 2?
(b) To go from state 1 to state 3 the small system must take 0.4 eV of energy and one particle (but no extra volume) from the reservoir. How many times more probable is it that the small system is in state 1 than state 3?
(c) To go from state 1 to state 4, the small system must take no energy but one particle and 10‒27 m3 of volume from the reservoir. How many times more probable is it that the small system is in state 1 than state 4?
