Question

A piston/cylinder arrangement has a linear spring and the outside atmosphere acting on the piston,. It contains water at 3 MPa, 400°C with the volume being 0.1 m³. If the piston is at the bottom, the spring exerts a force such that a pressure of 200 kPa inside is required to balance the forces. The system now cools until the pressure reaches 1 MPa. Find the heat transfer for the process. 

Answer 1

C.V. Water.

Continuity Eq.: m₂ = m₁ = m ;

Energy Eq : m(u₂ − u₁) = ₁Q₂ - ₁W₂ 

State 1: v₁ = 0.09936 m³/kg, u₁ = 2932.8 kJ/kg m = V/v₁ = 0.1/0.09936 = 1.006 kg 

Process: Linear spring so P linear in v. P = P₀ + (P₁ - P₀)v/v₁