A 60-gallon water heater is initially filled with water at 66°F. Determine how much energy, in Btu, needs to be transferred to the water to raise its temperature to 104°F. Given: The water properties at an average water temperature of 85ºF rho = 62.17 lbm/ft3 and cp = 0.999 Btu/lbm-R.

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Physics

Miley Rollins

27 September, 10:45

A 60-gallon water heater is initially filled with water at 66°F. Determine how much energy, in Btu, needs to be transferred to the water to raise its temperature to 104°F. Given: The water properties at an average water temperature of 85ºF rho = 62.17 lbm/ft3 and cp = 0.999 Btu/lbm-R.

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Abram · Answer 1

18930 Btu

Explanation:

The amount of heat needed to raise the temperature of a body of water is given by:

Q = m * cp * (tfin - ti)

The mass is the volume multiplied by the density

m = V * ρ

So

Q = V * ρ * cp * (tfin - ti)

The volume of water is 60 gallon, which is equivalent to 8.021 ft^3

Now:

Q = 8.021 ft^3 * 62.17 lbm / (ft^3) * 0.999 Btu / (lbm * R) * (104 R - 66 R) = 18930 Btu

Since we have a temperature difference we can convert Fahrenheit to Rankine