(5 %) Problem 16: Suppose a hot tub containing 1350 kg of water is heated from 1
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(5 %) Problem 16: Suppose a hot tub containing 1350 kg of water is heated from 100°C to 400°C. Note that the hot tub is being operated in part of the country where electricity is particularly expensive 50% Part (a) What is the cost, in dollars, of heating the hot tub, assuming 75.0% efficiency to account for heat transfer to the surroundings? The cost of electricity is 23 cents/kWh Grade Summar Deductions Potential cost 0% 100% Submissions sin cotan asin0 atan)acotan( cosh)tanh cotanhO) cosO tan() | | ( acos) sinhO 789 Attempts remaining: 20 (0% per attempt) detailed view 0 END °Degrees Radians (0 DEL CLEAR Submit Hint I give up Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. 50% Part (b) What current, in amperes, does the 220-V AC electric heater run on, if it took 3.9 h to heat up the water?Explanation / Answer
heat required to heat the water from 10 degrees to 40 degrees
Q = m*S*dT = (1350*4185*30) = 1.69*10^8 J = 1.69*10^5 kJ = 1.69*10^5 kW-s
Q = (1.69*10^5 )/3600 = 46.94 kWH
assuming 75% of efficiency
Q' = Q/0.75 = 46.94/0.75 = 62.58 KWH
Required cost is 62.58*23 =1439.34 cents =14.3934 $
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Power P = Q/t
P= 62.58/3.9 = 16.04 kW
But power P = V*I
current I = P/V = 16.04*10^3/220 = 72.90 A
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