What is the final pressure in the balloons after being disconnected?

[gruba]

Homework Statement

Two balloons are connected by a faucet.
Gas in the first balloon is at pressure $p_1=100kPa$, and in the second is $p_2=0,5MPa$.
Volumes are $V_1=0,12m^3$ and $V_2=0,5m^3$.
Temperature of a gas is constant.
Find pressure in balloons $p$ after faucet is opened (balloons are not connected).

Homework Equations

$pV=\frac{m}{M}RT$ - state of ideal gas

The Attempt at a Solution

State of gas before before balloons are disconnected is
$p_1V_1=\frac{m}{M}RT,p_2V_2=\frac{m}{M}RT$
and after balloons are disconnected is
$p(V_1+V_2)=\frac{2mRT}{M}\Rightarrow p=\frac{2p_1p_2}{p_1+p_2}=166,67kPa$.

Is this correct? How volumes $V_1$ and $V_2$ are not relevant in the equation for $p$?

 

[haruspex]

$p_1V_1=\frac{m}{M}RT,p_2V_2=\frac{m}{M}RT$

Are m and M the same for both?

 

[gruba]

Are m and M the same for both?

Mass of a balloon $m$ and atomic mass $M$ are not given. Could you elaborate how to set the equations
for finding the pressure $p$ in second case (disconnected balloons)?

 

[haruspex]

Mass of a balloon $m$ and atomic mass $M$ are not given. Could you elaborate how to set the equations
for finding the pressure $p$ in second case (disconnected balloons)?

You can assume M is the same for both, but not m. Assign two different unknowns. You have enough equations to cope with that.

 

[JustDerek]

I'm not sure as I'm only just learning this stuff myself though it appears I'm a couple of weeks behind you but wouldn't it be worth finding the mass flow rate? Sorry if that's wrong.

 

[haruspex]

I'm not sure as I'm only just learning this stuff myself though it appears I'm a couple of weeks behind you but wouldn't it be worth finding the mass flow rate? Sorry if that's wrong.

I read the question as asking about the final state, after flow has ceased and temperatures have returned to ambient.
(Otherwise there is not enough information.)