An immersion heater is connected to a 120 V power supply. Ittakes it 4 minutes t

Question

An immersion heater is connected to a 120 V power supply. Ittakes it 4 minutes to heat an 8 ounce cup of water from 15 C toboiling. Assuming no heat is lost to thesurroundings.
a) How much power is used by the heater? b) What's the resistance of the heater? An immersion heater is connected to a 120 V power supply. Ittakes it 4 minutes to heat an 8 ounce cup of water from 15 C toboiling. Assuming no heat is lost to thesurroundings.
a) How much power is used by the heater? b) What's the resistance of the heater?

Explanation / Answer

1 ounce = 0.02835kg So, mass of 8 ounce water = 8 * 0.02835 kg                                        m= 0.2268 kg Voltage V = 120 V time T = 4 min = 4 * 60 s = 240 s Initial temp t = 15 oC final temp t ' = 100 oC temp difference dt= t ' - t = 85 oC energy required to raise the water from t to t 'temperature is E = m C dt where C = specific heat of water = 4186 J /kg oC substitue values we get E = 80697.708 J power P = E / T               = 336.24 Watt (b). we know P = V^ 2 / R from this resistance of the heater R = V ^ 2 / P                                                      = 42.82 ohm

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