The time between switching off and on (the cooling time) depends upon the rate of heat loss. It is the time it takes to cool 5 C. You knoww that to be 3.0 minutes
The time it takes between switching on and off (the heating time) depends upon the time it takes to heat up 5 C, while the the heat loss is still going on.
You can get the heat loss rate from the 3 minute cooldown time, and the rate of heat addition from 4 kW figure.
Qloss = 24 kg * 4184 J/kg C * 5 C/180 s
= 2.79 kW
Qin = 4.00 kW
Qin - Qloss = 1.21 kW
Energy is lost at a rate that is 2.3 times faster than it can be added when the heat loss is still going on.
The heating cycle time will be 2.3 times 3 minutes, or 6.9 minutes
24 kg of water are heated by a thermostatically controlled 4Kw electric heater. The thermostat switches the heater on at 60 degree centigrade and off at 65 degree centigrade. If the time between switching off and switching on is 3.0 min, what will be the time between switching on and switching off. Assume that the rate of cooling of the water uniform over the range 60 degree centigrade to 65 degree centigrade.
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