1. Assuming you take a 10 minute shower in a shower with a modern showerhead whi

Question

1. Assuming you take a 10 minute shower in a shower with a modern showerhead which allows a flow of 2.5 gallons per minute, determine the mass of water used. Then, given that on average, water comes into your house at around 47°F, and your shower water is 120°F, determine how much energy is required to heat all of the water for your shower.

2. A new electric hot water heater claims to have dual 4500W copper heating elements. How long will it take to heat up enough water for your shower?

3. If you had no access to ice to put in a calorimeter, how could you account for heat transfer to the environment?

Explanation / Answer

1.

one gallon = 3.785 L

density of water = 103 kg/m3

mass of water used m = 10 x 2.5 x 3.785 x 10-3 x 103 = 94.625 kg

specific heat of water s = 4186 J/kgK

Energy required to heat this water E = m x s x (120 - 47) x 5/9 = 16.1 x106 J

2.

time taken by dual heating elements = E / 9000 = 1785 s

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