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Integrated Concepts(a) What is the cost of heating a hot tub containing 1500 $\mathrm{kg}$ of water from $10.0^{\circ} \mathrm{C}$ to $40.0^{\circ} \mathrm{C}$ , assuming 75.0$\%$ efficiency to account for heat transfer to the surroundings? The cost of electricity is 9 cents/kW ? h . (b) What current was used by the 220-V AC electric heater, if this took 4.00 h?

(a) $\operatorname{cost}=\$ 6.28$(b) $I=79.3 \mathrm{A}$

Physics 102 Electricity and Magnetism

Chapter 20

Electric Current, Resistance, and Ohm's Law

Current, Resistance, and Electromotive Force

Cornell University

Hope College

University of Winnipeg

Lectures

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So in this problem, we have a hitting top, and it contains water equal. Ah, when? 1005 100 kilograms. And we know that to the specific heat for water. See? Well, 4.2 times. 10 to the third. Ah, Joe. Put kilograms time. Sell says degrees. Right. And, uh, the temperature change from for this problem is from 10 degrees to 40 degrees, so we can calculate the total energy that we need for the water. So, uh, the water equal. See, Time's and time's that Atif. Right. So here, See, in this is AM and devotee of 30 degrees. So, uh, this is, uh so this is the water. This is a whole energy. That's what we need for the water. And, ah, the total energy that we need to keep the water is actually equal w defined by 75%. Right, because the efficiency is only 75%. So this is the total energy to heat the water. And remember that the unit for this wise actually in Joe's and the one key towards our they call 3.6 times into the six Jos. Right. So we need to use this video. Uh, divide buying 3.6 times 10 to 6 to transfer the unit from Joe's to Peter wants kill what's our and that we can see that this actually equal to 70 que towards our and, uh, for each kid awards our because this Ah, nine cent. Okay, so we can see that to the total cost. Booby. Ah, see a quote. 70 kill. What's our times? Nine cents. So this becomes, ah, $6.3. Okay. And in part B. So the key in process last for full analysts. So we wanted and the body is to 20 votes. So we wanted turning the the voltage in the process. So because we already know that energy equal 70 k towards power at kid was our and ah, last most four hours. So the power he'ii quot over tea equal 17.5. Uh, what's kiddo? What's Yeah. So we can determine the current I quote P D. Bye bye, v. Right, soapy 17.5. This is the unit is kill. What's so? It's a times 10 to the third. What's the ride by V. V is to 20 votes. So the solution is, uh, 79.5 and peers

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