Gas expansion

Two thermally insulated cylinders, A and B, of equal volume, both equipped with pistons,are connected by a valve. Initially A has its piston fully withdrawn and contains a perfect monatomic gas at temperature Ti, while B has its piston fully inserted, and the valve is closed. The thermal capacity of the cylinders is to be ignored. The valve is fully opened and the gas slowly drawn into B by pulling out the piston B; piston A remains stationary. Show that the final temperature of the gas is Tf = Ti/(2^(2/3))

So far i can gather that, as its a thermally isolated system, there is no change in heat, but work is done by slowly moving piston B.

So dU = dW = -pdV. And the equation of state is valid for before and after the expansion. So, assuming the valve has negligible volume,

(initial p)*V = Nk(initial T) and (final p)*2V = Nk(final T).

So i got 4 variables, and only two equations to work with at this stage. Any ideas?