Question

A water-filled reactor with volume of 50 ft³ is at 2000 lbf/in.², 560 F and placed inside a containment room,The room is well insulated and initially evacuated. Due to a failure, the reactor ruptures and the water fills the containment room. Find the minimum room volume so the final pressure does not exceed 30 lbf/in.².

Answer 1

C.V.: Containment room and reactor.

Mass: m₂ = m₁ = V_reactor/v₁ = 50/0.02172 = 2295.7 lbm 

Energy m(u₂ - u₁) = ₁Q₂ - ₁W₂ = 0 

⇒ u₂ = u₁ = 552.5 Btu/lbm

State 2: 30 lbf/in.², u₂ < ug  ⇒ 2 phase

u = 552.5 = 218.48 + x₂ 869.41 

⇒ x₂ = 0.3842 

 v₂ = 0.017 + 0.3842 x 13.808 = 5.322 ft³/lbm 

 V₂ = mv₂ = 2295.7 x 5.322 = 12218 ft³