€1 A particle can occupy one of three available energy levels: ε0 = 0, ₁ = aV or 2 = 2aV, where a is a fixed constant and V is the volume. a) State which ensemble could be used to describe 3 such particles with total energy E = 3aV, and use this ensemble to derive an equation of state for the pressure of this 3-particle system. b) State which ensemble could be used to describe N such particles with a fixed temperature T, and use this ensemble to derive an equation of state for the pressure of this N-particle system. c) State which ensemble could be used to describe a collection of such particles with a fixed. temperature T and chemical potential μ, and use this ensemble to derive an equation of state for the pressure and average number of particles in the system. d) Explain whether your answers to (a), (b) and (c) are consistent with each other and why.