Is it possible to have $\Delta T\neq 0$ with no heat exchange $Q=0$, no work $W=0$ done, and no change in internal energy $\Delta E=0$?

Question

Is it possible to have $Q=0$, $\Delta E=0$ and $W=0$, but $\Delta T\neq 0$?

In particular, if there is no change in internal energy, doesn't that imply it is an isothermal process, and therefore that $\Delta T=0$?

Answer 1

Consider a chemical reaction taking place in an adiabatic chamber of constant volume. Let's say the reaction is exothermic (releases heat).

Since the chamber is completely sealed, no energy enters or leaves the system in the firm of work or heat, and so the total energy change is also zero. But the reaction is releasing energy that was previously bound up in chemical bonds, and that energy has to go somewhere. It goes into increasing the vibrations of the molecules, increasing the temperature.

A physicist might consider this to be cheating, since if there's a chemical reaction then the system was not in equilibrium to start with, and the process is not quasi-static. If you impose thee additional reactions then I think you're probably right that the temperature can't change. At least, I can't think of any clever way to do it.

Answer 2

Assuming I've understood your requirements correctly magnetic cooling would count. The total internal energy doesn't change, but there is a redistribution of energy between the alignment of spins and lattice vibrations. That means the temperature can change without any interaction with the outside world.

Though maybe, like Nathaniel's answer, this is a bit of a cheat.

Answer 3

A simple elementary example of an isolated system for which $\Delta T \ne 0$ while both $\Delta U = 0$ and $W=Q=0$ is the case when two bodies at different temperatures initially are isolated but then internally connected via an effectively zero heat capacitance, zero mass heat conductors through which the bodies equilibrate and their temperatures equalize. Since the bodies and the connection between them are isolated from the outside neither heat nor work is exchanged, $Q=W=0$, and the total energy change is zero (it only gets redistributed between the bodies), $\Delta U = 0$, but the final temperature is different from that of the beginning temperature of either bodies, $\Delta T \ne 0$. This process of equilibration is, of course, not isothermal.