Room is heated by a base-board resistance heater, which is designed to heat the
ID: 2997654 • Letter: R
Question
Room is heated by a base-board resistance heater, which is designed to heat the air in this room from
8oC to 27 oC within 20 min.Approximating the room as a thermo-insulated cuboid 15m ? 10m ? 5m and assuming the specific heats to be constant at a room temperature (300K)
and pressure (100 kPa), please determine
(5a). (4p) The total mass of air inside the room, in kg.
(5b). (4p) The power required by the resistance heater, in kW.
Hints: It is assumed that there are no heat loss and air leakage for such a thermo-insulated room; air
can be considered as an ideal gas, and the specific heat can be assumed temperature-independent
(constant) for such a narrow temperature range involved; the kinetic energy and potential energy can
be ignored.
Explanation / Answer
Cp of air at 300k=1.005 Kj/Kg.K
Volume of the room=15*10*5=750 m3
Density of air=1.250 Kg/m3
a)
mass of air in room=m=density*volume=1.250*750=937.5 kg
b)
Q=1.005*mass of air*(27-8) Kj
=19.095*mass of air=19.095*937.5 KJ=17901.5625 KJ
Power=Q/t
t=20 min=20*60 s=1200 s
power=17901.5625/1200 KW=14.918 KW
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