Equalizing pressure between two vessels

[kandelabr]

Homework Statement

There are two insulated air containers, first with a volume V₁ and second with V₂. In the first there is a pressure p₁ and in the second p₂. The temperatures are the same in both, thus T. Then both containers are connected with a hose so that pressure equalizes, but no heat is transferred between them.
What are the final temperatures and final pressure?


2. Homework Equations
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The Attempt at a Solution

If there was heat transfer between containers, the final temperature would be the same in both and even the same as the temperature T in the beginning and because of that I could calculate the final pressure using pV = mRT (R = gas constant for air), where I'd get mass for one container from specific volumes.

But this case with no heat transfer is a bit confusing. I can't get final pressure with the equation used above because I don't know the final temperatures. The book says the final pressure is the same as above, but I don't know why is it so.

 

[kandelabr]

My results regarding the case where heat transfer occurs are that entropy actually decreases - using this formula:

s = C_vln(p_end/p1) + C_pln(v_end/v₁) +
+ C_vln(p_end/p₂) + Cpln(v_end/v₂),

where v₁ and v₂ are specific volumes before mixing and v_end is the final specific volume (the same for pressures).

The actual numbers are:
T = 293 K
p₁ = 1 bar
p₂ = 20 bar
V₁ = 5m³
V₂ = 2m³

From that I got
v₁ = 0.8403 m³/kg)
v₂ = 0.0420 m³/kg)
p_end = 6.43 bar
v_end = 0.1308 m³/kg

s = -206 J/kgK

I know entropy cannot be decreased with mixing, so what's wrong here?