Question

It is interesting to consider why sufficiently slow work does not tend to increase entropy. We can model atoms as a collection of quantum particle-in-a-box’s; Compression work will tend to squeeze the size of these quantum boxes, reducing L.

i) First, suppose that you squeeze the quantum box; What effect will a slight reduction of L have on the energy states of the particle-in-a-box? What effect would this have on what energy states the enclosed particle can inhabit (i.e. does squeezing a quantum box push a particle out of the ground state)? What effect would this have on the entropy?

ii) Now, suppose instead that you left this quantum particle-in-a-box next to a second “hot” particle-in-abox; What effect would this have on the energy states of the original particle-in-a-box? What effect would this have on what states the particle can inhabit? What effect does this have on the entropy?

iii) Finally, suppose that you rapidly squeeze the particle-in-a-box; What effect would this have on the energy states of the particle-in-a-box? What effect would this have on what state the enclosed particle can inhabit? What effect does this have on the entropy?

Answer 1