A well-sealed room contains 90 kg of air at 1 atm and 20°C. Now a 1-kW electric heater and a 200-W fan are turned on. If heat transfer through the walls is negligible, the air temperature in the room in 15 min will be
A)36.7°C
B)31.9°C
C)33.9°C
D)20.3°C
E)49.5°C

Question

Quizplus · Accepted Answer

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R=0.287 "kJ/kg.K"
Cv=0.718 "kJ/kg.K"
m=90 "kg"
P1=1 "atm"
T1=20 "C"
We=1 "kJ/s"
time=15*60 "s"
Wfan=0.2 "kJ/s"
"Applying energy balance E_in-E_out=dE_system gives"
time*(Wfan+We)=m*Cv*(T2-T1)
"Some Wrong Solutions with Common Mistakes:"
Cp=1.005 "kJ/kg.K"
time*(Wfan+We)=m*Cp*(W1_T2-T1) "Using Cp instead of Cv "
time*(-Wfan+We)=m*Cv*(W2_T2-T1) "Subtracting Wfan instead of adding"
time*We=m*Cv*(W3_T2-T1) "Ignoring Wfan"
time*(Wfan+We)/60=m*Cv*(W4_T2-T1) "Using min for time instead of s"

A Well-Sealed Room Contains 90 Kg of Air at 1