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

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