Question

An insulated cylinder/piston has an initial volume of 0.15 m³ and contains steam at 400 kPa, 200°C. The steam is expanded adiabaticly, and the work output is measured very carefully to be 30 kJ. It is claimed that the final state of the water is in the two-phase (liquid and vapor) region. What is your evaluation of the claim?

Answer 1

C.V. Water. Energy

Eq. m(u₂ − u₁) = ₁Q₂ − ₁W₂ 

Entropy Eq : m(s₂ − s₁) = ∫ dQ/T Process: ₁Q₂ = 0 and reversible 

State 1: (T, P)  v₁ = 0.5342, u₁ = 2646.8, s₁ = 7.1706 kJ/kg K

m = V₁/v₁ = 0.15/0.5342 = 0.2808 kg

With the assumed reversible process we have from entropy equation

s₂ = s₁ = 7_.1706 kJ/kg K and from the energy equation

_{u2 = u1 − 1}W₂/m = 2646.8 - 30/0.2808 = 2540.0 kJ/kg

State 2 given by (u, s) check 

 s_G (at u_G = 2540) = 7.0259 < s₁

⇒ State 2 must be in superheated vapor region.