Question

Five kilograms of steam initially at 1.40 MPa and 650 °C are reversibly and adiabatically expanded to T^sat= 40 °C. Determine the quality of the steam in its final state and the work required.

(C_p=33.59 J/mole-K C_V=25.275 J/mole-K)

.

Answer 1

Inlet state at 1.40 MPa and 650 °C = superheated steam

Outlet state 40 °C = saturated steam

Specific Entropy of Superheated Steam S = 7.998 kJ/kg-K

Specific Entropy of Saturated Steam Sg = 8.255 kJ/kg-K

Specific Entropy of Saturated Water Sf = 0.5724 kJ/kg-K

Entropy balance

In reversibly and adiabatically expansion

Entropy intlet = entropy outlet

S = xSg + (1-x)Sf

7.998 = x * 8.255 + (1-x)*0.5724

x = (7.998 - 0.5724) / (8.255 - 0.5724)

Quality of steam x = 0.97

Enthalpy of inlet steam H1 = 3807.85 kJ/kg

Enthalpy balance at outlet

H2 = xHg + (1-x)Hf = 0.97*2573.54 + 0.03*167.541

H2 = 2501.36 kJ/kg

Work required W = m (H2 - H1)

= 5 kg x (2501.36 - 3807.85) kJ/kg

= - 6532.45 kJ