Question

How much work can be obtained from an adiabatic, continuous-flow turbine, if steam at 60 bar and 500^oC is used and the outlet stream is at 1 bar and 400^oC?

(a) -144 kJ/kg

(b) -155 kJ/kg

(c) -166 kJ/kg

(d) -177 kJ/kg

I had been asked this question in an international level competition.

This interesting question is from Energy Balance Numericals Without Reactions topic in portion Energy Balance of Bioprocess Engineering

Answer 1

The correct choice is (a) -144 kJ/kg

The explanation is: Basis: 1 kg steam

For superheated steam:

Inlet: (60 bar, 500°C) h1 = 3422 kJ/kg

Outlet: (1 bar, 400°C) h2 = 3278 kJ/kg

min = mout = 1 kg

DECV + Sni(Ek + Ep + H)i = Q + WS (General form of the energy balance)

Now we make the following simplifying assumptions for this turbine:

▪ Adiabatic: Q = 0

▪ The inlet and outlet lines are not tremendously different in height: Ep = 0

▪ There is little difference in the velocity of the fluid in the inlet and outlet lines: Ek = 0

▪ There are no accumulation terms (steady-state operation with steady flow): DECV = 0

The simplified form of the energy balance is therefore:

Hout – Hin = Ws = mouthout – minhin = m(hout – hin)

Substituting in the values for the specific enthalpies gives:

Ws = m (hout – hin) or Ws/m = (3278 – 3422) kJ/kg = -144 kJ/kg.