A small immersion heater can be used in a car to heat a cup of water for coffee

Question

A small immersion heater can be used in a car to heat a cup of water for coffee or tea. If the heater can heat 120 mL of water from 25 degree C to 95 degree C in 7.5 min. Assume the manufacturer's claim of 87 percentage efficiency. The specific heat of water is 4186 J/(kg degree C). Approximately how much current does it draw from the cat's 12-V battery? Express your answer to two significant figures and include the appropriate units. I = What is its resistance? Express your answer to two significant figures and include the appropriate units R =

Explanation / Answer

first we find the amount of heat energy

Q=ms[t2-t1]=120*10^-3*4186*[95-25]=35162.4 J

efficiency=87%

now we find the work done

efficiency =work/heat

87/100=work/35162.4

work=30591.288 J

now we find the power of given body

power=work/time=30591.288/7.5*60=67.981 W

part A:

let us find the current

current I=power/voltage=67.981/12=5.67 A

part B:

the resistance R=voltage/current

=12/5.67=2.12 ohms

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