Question

A 150 L (= 40 gal) electric hot-water tank has a 5.0 kW heater. How many minutes will it take to raise the water temperature from 61.0 F to 151 F? Express your answer with the appropriate units.

Answer 1

change in temperature of water =(151-61)F =90F

conversion from Fahrenheit to Celcius = (5/9)90 =50⁰ C

-> To heat one 1 kg of water 1C requires 4186 J.

-> 1 gallon of water = 62.4 * 231/1728 lbs = 8.341 lbs = 3.79 kg.

-> So you need 15865 J to raise 1 gallon of water 1C.

We want to raise the temperature of 150L(40 gallons) = 50⁰ C.

=> That takes= 15857*50*40 = 31714000 Joules.

-> A joule is one watt-second. The heater provides 5000 watts.

So we divide the 3,17,14,000 watt-seconds by 5000 watts and we get 6342 seconds = 1hr 45 min approximately