A heat exchanger is used to heat cold water at 8°C entering at a rate of 1.2 kg/s by hot air at 90°C entering at rate of 2.5 kg/s. The heat exchanger is not insulated, and is loosing heat at a rate of 28 kJ/s. If the exit temperature of hot air is 20°C, the exit temperature of cold water is (use constant specific heats at room temperature)
A)43.1°C
B)48.6°C
C)78.0°C
D)37.5°C
E)27.5°C

Question

Quizplus · Accepted Answer

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C_w=4.18 "kJ/kg-C"
Cp_air=1.005 "kJ/kg-C"
Tw1=8 "C"
m_dot_w=1.2 "kg/s"
Tair1=90 "C"
Tair2=20 "C"
m_dot_air=2.5 "kg/s"
Q_loss=28 "kJ/s"
"The rate form of energy balance for a steady-flow system is E_dot_in = E_dot_out"
m_dot_air*Cp_air*(Tair1-Tair2)=m_dot_w*C_w*(Tw2-Tw1)+Q_loss 
"Some Wrong Solutions with Common Mistakes:"
m_dot_air*Cp_air*(Tair1-Tair2)=m_dot_w*C_w*(W1_Tw2-Tw1) "Not considering Q_loss"
m_dot_air*Cp_air*(Tair1-Tair2)=m_dot_w*C_w*(W2_Tw2-Tw1)-Q_loss "Taking heat loss as heat gain"
(Tair1-Tair2)=(W3_Tw2-Tw1) "Equating temperature changes of fluids"
Cv_air=0.718 "kJ/kg.K"
m_dot_air*Cv_air*(Tair1-Tair2)=m_dot_w*C_w*(W4_Tw2-Tw1)+Q_loss "Using Cv for air"

A Heat Exchanger Is Used to Heat Cold Water at 8°C