Current drawn from car battery to heat up water

[confusedbyphysics]

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 C to 95 C in 8 minutes, a) approximately how much current does it draw from the car's 12-V battery, and b) what is its reistance? Assume the manufacturer's claim of 60% efficiency.

My work:

T(f) - 95 C T(i)= 25 C
t = 8 min = 480 s
V= 12 V
volume = .12 L

First I converted .12 L to kg using density of water, comes out .12 kg.

Then I used the relationship between heat transfer and temperature change equation Q= mcT, specific heat of water is 4186 J/kg Cel

Q = .12kg (4186 J/kgC) (95 C-25 C) = 35162.4 J to heat the water.

Then I used the power equation, Power = work/time = 35162.4 J / 480 s = 73 Watts

Then I used I = P/V, Electric Current = Power / voltage = 73 W/12 V = 6.1 A

The answer in the back of the book says 10 A. I got 6.1 A, which if rounded up could be 10 A and it does say approximately, but I'm not sure if I did this right at all and if my work is wrong he will check it wrong. Am I doing this right or wrong? If wrong, what should I do?? And I'm not sure where the efficiency comes in? Thanks for any help

 

[andrevdh]

Only 60% of the input power (or energy) is converted to heat by the resistor, that is
$$0.6P_{input}=P_{resistor}$$

 

[kyle8921]

!

Your calculations seem to be correct, but there are a few things to consider. Firstly, the efficiency of the immersion heater needs to be taken into account. The manufacturer claims 60% efficiency, which means that only 60% of the energy drawn from the battery is actually used to heat the water. Therefore, the actual current drawn from the battery will be higher than your calculated 6.1 A. To account for efficiency, you can divide the calculated power (73 W) by the efficiency (0.6) to get the actual power needed from the battery (73 W / 0.6 = 122 W). Then, using the same equation I = P/V, the actual current drawn from the battery would be 122 W / 12 V = 10.2 A. This is closer to the answer in the book.

Additionally, the resistance of the immersion heater can be calculated using the formula R = V/I, where V is the voltage (12 V) and I is the actual current drawn from the battery (10.2 A). This would give a resistance of approximately 1.18 ohms.

In summary, your calculations are correct, but to get a more accurate answer, you need to take into account the efficiency of the immersion heater. Also, make sure to check the units in your calculations (e.g. converting volume to mass in kg). Keep up the good work!