Question

The faucet across from my office has been leaking hot water. In exactly four minutes I filled a Pepsi bottle that holds 20 fl oz. I measured the temperature of the hot water at 118.4F, the cold water tap read 54.4F. How much power (in W) is this leak using assuming no loss from the efficiency of the boiler or in transmission? What are realistic losses in a real system? What is the extra energy doing in the building?

For an Energy and the Environment course.

Answer 1

Volume of water = 20 fluid ounce = 20/33.8 litre = 0.592 litre = 0.000592 m³    ( since 1 fluid once = 33.8 litre)(1 litre = 0.001 m³ )

density of water = 1000 kg/m³

so mass of water = m = density x volume = 0.000592 x 1000 = 0.592 kg

Specific heat of water = 4186 J/kgK

temperature of cold water = T_c = 54.4 F = 285.6 K

temperature of hot water = T_h = 118.4 F = 321.1 K

change in temperature = 35.5 K

Heat can be given as ::

time = t = 4 min = 4 x 60 sec = 240 sec

So Power is given as