A hot water leak in one of the faucets can be very wasteful in energy. Assume th

Question

A hot water leak in one of the faucets can be very wasteful in energy. Assume that there is a slow leak of 0.5 gpm (gallons/min) near the faucet (assume temperature of 160 degree F) and the cold water mains temperature is 70 F. How much energy in Btu/hr is wasted if the water tank heated by natural gas. Assume a typical efficiency of a gas water heater of 0.9 and the loss in the water distribution to be 0.8. How much energy in Btu/hr is wasted if heated by electricity. Assume a typical efficiency of an electric water heater of 0.95 and the loss in the water distribution to be 0.8. Is this a fair comparison? Briefly discuss.

Explanation / Answer

(a)

Leakage per hr = 0.5*60 = 30 gallons

Specific heat of water = 1

Weight of 1 gallon of water = 8.33 lbs

Therefore, total energy waste in case of natural gas =m*Cp*dT/(overall efficiency) = (30*8.33)*(1)*(160-70)/(0.9*0.8) = 31237.5 Btu/hr

(b) Total energy waste in case of electric water heater =m*Cp*dT/(overall efficiency) = (30*8.33)*(1)*(160-70)/(0.95*0.8) = 29593.4Btu/hr

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