If the heater can heat 200 mL of water from 22 ∘C to 91 ∘C in 13.9 min , approximately how much current does it draw from the car’s 12-V battery? Assume the manufacturer’s claim of 75% efficiency. Express your answer using two significant figures.

Explanation:

First, we will convert 200 ml into kg as follows.

200 ml = 0.2 kg

Now, we will take the density of water as 1 g/ml.

And, dT = [tex](91 – 22)^{o}C[/tex]

= [tex]69^{o}C[/tex]

Also, we know that specific heat of water is 4.186 [tex]kJ/kg^{o}C[/tex]. Therefore, we will calculate the heat energy as follows.

q = [tex]mC \Delta T[/tex]

= [tex]0.2 kg \times 4.186 kJ/kg^{o}C \times 69^{o}C[/tex]

= 5.77 kJ

Now, we will calculate the power delivered as follows.

P = [tex]\frac{Q}{t}[/tex]

= [tex]\frac{5.77 kJ}{13.9 \times 60}[/tex]

= 69.1 W

It is given that efficiency is 75%. Therefore, input power will be calculated as follows.

[tex]P_{input} = \frac{69.1}{75} \times 100[/tex]

= 92.13 W

Now, we will calculate the current as follows.

P = [tex]V \times I[/tex]

I = [tex]\frac{92.13 W}{12 V}[/tex]

= 7.67 A

Therefore, we can conclude that current drawn from the car’s 12-V battery is 7.67 A.

Explanation:First, we will convert 200 ml into kg as follows.

200 ml = 0.2 kg

Now, we will take the density of water as 1 g/ml.

And, dT = [tex](91 – 22)^{o}C[/tex]

= [tex]69^{o}C[/tex]

Also, we know that specific heat of water is 4.186 [tex]kJ/kg^{o}C[/tex]. Therefore, we will calculate the heat energy as follows.

q = [tex]mC \Delta T[/tex]

= [tex]0.2 kg \times 4.186 kJ/kg^{o}C \times 69^{o}C[/tex]

= 5.77 kJ

Now, we will calculate the power delivered as follows.

P = [tex]\frac{Q}{t}[/tex]

= [tex]\frac{5.77 kJ}{13.9 \times 60}[/tex]

= 69.1 W

It is given that efficiency is 75%. Therefore, input power will be calculated as follows.

[tex]P_{input} = \frac{69.1}{75} \times 100[/tex]

= 92.13 W

Now, we will calculate the current as follows.

P = [tex]V \times I[/tex]

I = [tex]\frac{92.13 W}{12 V}[/tex]

= 7.67 A

Therefore, we can conclude that

current drawn from the car’s 12-V battery is 7.67 A.