Two chambers are interconnected by a valve

[Fatima Hasan]

Homework Statement

Two chambers, 10 m3 each, are interconnected by a valve, as shown in the figure, with one chamber containing air at 2500 kPa and 287°C and the other chamber is evacuated. The valve is now opened and the air reaches a mechanical equilibrium and a thermal equilibrium with the surroundings at 15°C. Determine (a) the final pressure, (b) the final temperature of air, (c) the total change in internal energy, and (d) the amount of heat transfer.

Relevant Equations

Here is my work :
State 1 :
A
V1A = 10 m^3
P1A = 2500 kPa
T1A = 560 K
m1A = P1A * V1A / (T1A *R)
m1A = 155.5 kg
B
V2A = 10 m^3
m2A = 0 kg
State 2 :
T = 15+273 = 288 K , and that's the final temperature ? ( not sure about that , because it's given and the question in part (b) asks to get the final temperature )
m2 = m1A + m2A
m2 = 155.5 kg
V2 = V1A + V2A
V2 = 10 + 10 --> = 20 m^3
P2 = m2 * R * T / V2
P2 = 642.6504 K Pa ( the final pressure )
Since there are no heat and work interactions ,
c) = 0
d) = 0
Could someone check my answer please ?

 

[scottdave]

If there was zero change in internal energy, can you explain the temperature change to be "equal to the surroundings"?