First Law of Thermodynamics help

1. The problem statement, all variables and given/known data

Steam flow through a pipe at a pressure if 8bar and a temperature of 340C. A valve is opened and steam is allow to enter an insulated enclosure whose volume is 0.5(m^3), until the pressure equals the quantity of steam that enters the enclosure.

2. Relevant equations

Q – W + ∑MIN(hIN+(v2IN)/2+gzIN) – ∑mOUT(hOUT+(v2OUT)/2+gzOUT) = m2(u2+(v22)/2+gz2) – m1(u1+(v21)/2+gz1)

3. The attempt at a solution

(Here is where I’m not sure)

I know that:

gz = 0 for all

And I would have thought that because up until the pressure in the chamber is equivalent to the mass of the steam, mOUT would be zero, as the steam is only coming in.

I also THINK that Q is 0 because no heat is being added to the system, and W is zero because there is no mechanical reactions.

However, what I don’t understand is the answer says that m1 is 0 (why? Is this because the only input is mIN?), vIN is 0 (is this because of the equivalence of v1 and vIN?)

The next step in the solution is

mINhIN = m2u2

And is it right that mIN and m2 will be equivalent based of continuity?

Thanks for any help as I am alright with using steam tables and interpolation later
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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