A hot water stream at 80 C enters a mixing chamber with a mass flow rate of 0.5 kg/s where it is mixed with a stream of cold water at 20 C. If it is desired that the mixture leae the chamber at 42 C, determine the mass flow rate of the cold-water stream. Assume all the streams are at pressure of 250 kPa. Answer : 0.865 kg/s

0.865kg/s

Explanation:

This is a question of energy balance. Assuming that the specific heat of all the streams is constant, we can write a mass flow rate balance for the streams;

Mass flow rate in = Mass flow rate out

m1 + m2 = m3

Also m1. h1 + m2. h2 = m3. h3

m1T1 + m2T2 = (m1 + m2) T3

Let m2 be the mass flow rate of cold water.

m2T2 = m1T3 + m2T3 - m1T1

m2T2 - m2T3 = m1 (T3-T1)

m2 (T2-T3) = m1 (T3-T1)

m2 = m1 (T3-T1) / (T2-T3)

m2 = 0.5 (42-80) / (20-42)

m2 = 0.865kg/s