Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well insulated 10-gallon tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for analysis.
GIVEN
- Two electric resistance heaters with l=0.2 m and d=0.02 m
- V=10 gallon= 37.85 liter of water at T0 =300 K
- Each heater power= 500 W
FIND
(a) Time required for bringing water temperature in the tank to Tf =340 K.
(b) State the assumption for analysis.
ASSUMPTIONS
- Steady state heat transfer
- All the heat dissipated through the heater is gained by water.
- There is uniform mixing of fluid maintaining same temperature at each point at given time.
PROPERTIES AND CONSTANTS
Specific heat(cp)= 4177 J/(kg K)
Density(?) = 989 kg/m3
Total energy required for heating 10 gallons of water from 300 to 340 K is
Power generated through two electric resistance heaters P=2*500 W= 1 KW.
Thus,
Total time required to heat the water =Q/P sec
=6107.57/1 sec
=6107 seconds
= 1.7 hours.
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