# pulmonary physics: balloons in closed chambers

Imagine we have an expanded balloon with radius $R_1$ and an internal pressure of $+20$ atm, in an room at $0$ atm of pressure. The system is at equilibrium. Now, I drop the pressure in the room to $-50$ atm. What happens then?

I don't think there is a unique solution to the problem as stated. First, at equilibrium, the net pressure across the balloon interface has to be $0$, so there has to be a $20$ atm elastic recoil force that wants to collapse the balloon. Once again after giving sufficient time to equilibrate, post $-50$ atm drop, you have a net pressure across the balloon interface of $0$ where $P_{\text{elastic recoil}}=P_\text{internal}-P_\text{external}$. If you only know the external pressure, you are left with two variables. Laplace's law does relate elastic recoil pressure to internal pressure if you know the radius, but you don't know the radius after the change. You can't use Boyle's law here either because you don't know the external pressure change and you don't have the radius to determine the volume change. Thoughts?