$**14\mathrm{.}5.$ A question arose among a group of students concerning a gas expanding by an adiabatic process and at the same time doing no work. One part of the group thinks the process must be isothermal, while the other part insists it cannot be isothermal. They ask you to straighten this matter out.

a$.$ Explain under what circumstances the process will be isothermal.

b$.$ Explain under what circumstances it will not be isothermal.