Question

Liquid water at 15 ℃ is heated by mixing it with saturated steam at the same pressure. Liquid water enters a chamber at a rate of 4.3 kg/s and saturated steam enters at a rate of 0.17 kg/s. The mixture leaves the mixing chamber as a saturated liquid at 40℃. If the surroundings are at 15℃, determine (a) the temperature of the saturated steam entering the chamber, (b) the exergy destruction during this mixing process, and (c) the second-law efficiency of the mixing chamber. Hint: You must look up the second-law efficiency of a mixing chamber.

Answer 1

a) Let the enthalpy of saturated steam be h₁

h₂ be enthalpy of  liquid water at same pressure

The heat balance of mixer can be written as

= mass flow rate of saturated steam =0.17 kg/s

= mass flow rate of liquid water at 15⁰C= 4.3 kg/s

h₂₌ enthalpy of liquid water at 15⁰C

h₃= enthalpy of saturated water at 40⁰C= 167.54 kJ/kg

Hence

By trial and error

Pressure, p=400 kPa

h₁= 2738.06 kJ/kg

h₂= 63.34 kJ/kg

Hence Temperature of saturated steam ai inlet(p=400kPa) is

T₁= 143.61⁰C

b) The exergy destruction is given by

Where

T₀= surrounging temperature= 15+273=288 K

S_gen= entropy generation

Hence exergy destruction is

c) The second law efficiency is defined by(without work and heat transfer)

Where

= availability which is defined by

V₀ and V are belocities at dead state and process conditions respectively(neglected)

z₀ and z are static heads at dead state and process conditions respectively (neglected)

h₀ = enthalpy at dead state of 15 ⁰C and p=101.3 kPa= 63.36 kJ/kg

s₀= entropy at dead state= 0.2244 kJ/kg-K

= availability supplied

=availability produced

Hence