Question

Assume an average person uses about 20 gallons of hot water each day. Assume the water temperature must be raised from 50 degrees F to 120 degrees F, how many Btus of energy are used? What is the cost for fuel (at 10$ per Mbtu) for you shower or bath?

1 gal of water = 8.3lbs.

1 Mbtu = 1000 Btus

1 Btu = amount of heat to raise one pound of water by 1 degree F

Answer 1

Answer:

Let us go to the basics first.

We know that anount of energy required to heat water is given by following relation:

Amount of energy = mcdt [m=mass of water =20 gallons = 20*8.3 lbs = 166 lbs = 166*0.453 kg = 75.3 kg; c=specific heat of water = 4187 J/kg°C; dt= temperature difference = 120 F - 50 F = 48.9°C - 10°C =38.9°C]

=>Amount of energy = mcdt

=>Amount of energy = 75.3*4187*38.9 = 12264434.8 J = 12264434.8*0.000948 BTU = 11624.4 BTU (Answer)

Thus, cost of fuel = 11624.4 BTU * $10 / MBTU

=>cost of fuel = 11624.4 BTU * $10 / 1000BTU

=>cost of fuel = $116.24 (Answer)