Imagine a gas made up entirely of negatively charged electrons. Like charges repel, so the electrons exert repulsive forces on each other. Would you expect that the temperature of such a gas would rise, fall, or stay the same in a free expansion? Why?

The temperature would fall.

Explanation:

The question can be solved by using first law of thermodynamics.

The law states:

The change in internal energy of the system is equal to the heat energy supplied to the system minus the workdone by the system.

ΔU = Q - W

where ΔU is change in internal energy of the system

Q is energy given to the system

W is workdone by the system

Because the charges are repelling each other it means they will move away from each other and their repulsive forces will do positive workdone (workdone is defined as distance moved in the direction of the force applied). Therefore W > 0.

There is no energy supplied to the system so Q = 0.

Using the relation ΔU = Q - W we can see that if Q = 0 and W > 0 then ΔU < 0. Hence internal energy of the system falls so the temperature falls.