I just started studying statistical mechanics and I'm doing a multiple choice quiz but I'm confused about one (well, two) questions in particular. The main one is the following:
"A microcanonical ensemble of systems corresponds to a collection of systems:
Select one or more: (a) All having a different macrostate. (b) All with the same energy. (c) In every different microstate. (d) All having the same microstate."
I know that by definition a microcanonical ensemble has a constant total energy, which leads me to think that b is an answer, but then the answer would refer to the 'collection of systems all having the same energy'. If by collection it means the individual microstates then I don't think this is true as I'm pretty sure the microstates don't all have the same energy. Also, I think that c is correct too since the microstates aren't identical but I don't really know what it means by 'in every different microstate'. Any help will be greatly appreciated!
Edit: Sorry, I forgot to include the other one I was a bit unsure of as well. It is to do with a system in contact with a heat bath, i.e. the canonical ensemble. The question says:
"A system in contact with a heat bath has: (a) The same temperature as the heat bath. (b) A constant mean internal energy. (c) The same energy as the heat bath. (d) A fixed, constant internal energy."
I know that (a) is definitely one of the answers, and I am sure that (c) can't be an answer because on Wikipedia it says that 'The system can exchange energy with the heat bath, so that the states of the system will differ in total energy.' which means the system surely can't have the same energy as the heat bath. So that leaves either (b) or (d). My notes say that in the case of a canonical ensemble 'we should now talk about an average energy $\bar E$ rather than $E$' so according to that it should be (b) but I'm struggling to distinguish between b and d really.