say you have a thermally insulated box which is separated into equal parts by a thermally insulated piston (frictionless) and each part has the same number of molecules and both sides are both at the same initial temperature, pressure, and volume and have the same constant heat capacity at constant volume (Cv=5/2Nk)
assume somehow you can slowly heat one side until its pressure doubles, what is the effect on each side's temperature and volume?
The Attempt at a Solution
if pressure goes up then volume can go down or temperature can increase or some combination of the two, so the heated side should either get smaller or get warmer if the pressure doubles. but there isn't anything that would do compression work on the heated side, so it doesnt seem like it should get smaller.
how you can know how each of the variables changes independently of each other on either side. seems like the heated side could increase in pressure by increasing in temperature at constant volume or by increasing in volume a bit and increasing in temperature even more. same for the other side
is there a way to know how temp/volume on each side change independtly of each other or can you only deal with ratios of the variables