An insulated mixing chamber, operating at steady-state, mixes superheated water

Question

An insulated mixing chamber, operating at steady-state, mixes superheated water vapor (stream 1) and saturated water vapor (stream 2) at equal mass flow rates. The mixing process involves no work. Both streams are at 200 kPa as they enter the mixing chamber, and the mixed stream (stream 3) leaves at 200 kPa. The temperature of the superheated vapor is 600 K. The temperature and pressure of the room in which the tanks sits are 300 K and 100 kPa, respectively.

a. Determine the exergy destroyed in the process per mass flow rate out of the chamber

i. Using the 2nd law.

ii. Using an exergy (availability) balance.

b. Determine the specific flow exergy of stream 2.

Explanation / Answer

Using energy avialbility balance

Energy of stream 1 + Energy of stream 2 - Q = energy of stream 3

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

from steam tables at stream 1 super heated vapor at 200 kpa h2 = 2.7 x 10 ^6 j/kg

h1 at saturated vapour at 200 kpa h1 = 3.126 x 10 ^6 j/kg

in ths case mass flow rate is same

m1 = m2

hence substituting the values in the energy equation

3.126 x10^6 + 2.7 x10^6 - 2 q = 2 x 2.7 x 10 ^6

energy destroyed in the process per mass flow rate out of the chamber q = 0.213 j/kg

using second law

Change of entropy during heat transfer = Q1 / T1

= Q /600

Change of entropy during heat transfer = Q2/300

Q1 +Q2 = q

Available energy with system =( 600 - 300 )2

= 600 kj

Specific flow of energy

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