A 10 kg/s stream of super-heated steam at 240 C and a stream of saturated liquid

Question

A 10 kg/s stream of super-heated steam at 240 C and a stream of saturated liquid water are combined in a mixing heat exchanger and a stream of saturated vapor exits, with all three streams at p=10 bar as shown in the diagram below. I can be assumed that the heat exchanger is adiabatic, the changes in kinetic and potential energy are negligible, and the environment is at T0=25 C.

a) What is the mass flow rate at 2, m2?

b) What is the mass flow rate at 3, m3?

c) How much entropy is generated during the process, Sgen?

(pleas show/explain all steps/work)

Explanation / Answer

Heat added from 2-3 equals heat lost from 1-3.

m1(h1-h3) = m2(h3-h2)

h1 = h(240 degrees C, 10 bar) = 2920.4 KJ/kg

h2 = hf(10 bar) = 762.81 KJ/kg

h3 = hg(10 bar) = 2778.1 KJ/kg

a) m2 = (m1(h1-h3))/(m2(h3-h2) = 0.706 kg/s

b) m3 = m1 + m2 = 10 kg/s + 0.706 kg/s = 10.706 kg/s

Sgen = m3s3 - m1s1 - m2s2

s1 = s(240 degrees C, 10 bar) = 6.8817 KJ/kg*K

s2 = sf(10 bar) = 2.1387 KJ/kg*K

s3 = sg(10 bar) = 6.5863 KJ/kg*K

c) Sgen = 10.706*6.5863 - 0.706*2.1387 - 10*6.8817 = 0.186 KJ/K*s

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