In class, I mentioned how you can calculate the energy needed to heat a pool usi

Question

In class, I mentioned how you can calculate the energy needed to heat a pool using the same type of calculations we used when plotting the Temp vs heat (q) for a mole of water from ice to steam. For this problem, we'll now turn our attention to a Jacuzzi, aka a hot tub. Suppose a backyard Jacuzzi hold 2.00 cubic meters of liquid water that is initially at 25 degrees Celsius. Calculate how much heat (in Joules) would be needed to raise the temperature to very comfortable 40 degrees Celsius. You should have this in your notes already, but I will include that there are 1000 L in one cubic meter and that you can assume that water has a density of 1.00 kg/L.

Explanation / Answer

volume of water = 2.00 m3

volume of water = 2 x 1000 L

mass of water = volume x density

                       = 2000 x 1

                        = 2000 kg

Q = m Cp dT

    = 2000 x 10^3 x 4.184 x (40 - 25)

   = 1.25 x 10^8 J

heat needed = 1.25 x 10^8 Joles

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