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4 December, 17:30

The heating element of a water heater in an apartment building has a maximum power output of 37 kW. Four residents of the building take showers at the same time, and each receives heated water at a volume flow rate of 11x10-5 m3/s. If the water going into the heater has a temperature of 14°C, what is the maximum possible temperature of the hot water that each showering resident receives

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  1. 4 December, 20:47
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    maximum possible temperature is 34.088°C

    Explanation:

    Given data

    power output Q = 37 kW

    volume flow rate = 11 x 10^-5 m3/s

    temperature t = 14°C

    to find out

    maximum possible temperature T

    solution

    we can say

    total water volume = 4 residents * volume flow

    total water volume = 4 * 11 x 10^-5 = 44 * 10^-5 m³/s

    so we say total water mass = 1000 * volume

    total water mass = 1000 kg/m³ * 44 * 10^-5

    total water mass = 0.44 kg

    we know

    dQ/dt = (dm/dt) * (S) * (T - t)

    so here we know specific heat of water S = 4.186 joule/gram °C

    37 = 0.44 * 4.186 * (T-14)

    T = 34.088°C

    maximum possible temperature is 34.088°C
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