Question

The heating element of a water heater in an apartment building has a maximum power output of 30 kW. Four residents of the building take showers at the same time, and each receives heated water at a volume flow rate of 1.49 10-4 m3/s. If the water going into the heater has a temperature of 10° C, what is the maximum possible temperature of the hot water that each showering resident receives

Answer 1

Answer:

22.02°C

Explanation:

P = Power output = 30 kW

Volume flow rate of water = $1.49\times 10^{-4}\ m^3/s$

S = Specific heat of water = 4.186 kJ/mol°C

$T_i$ = Initial temperature = 10°C

$T_f$ = Final temperature

Total volume of water is

$v=4\times 1.49\times 10^{-4}\\\Rightarrow v=5.96\times 10^{-4}\ m^3/s$

Mass flow rate is

$m=\rho\times v\\\Rightarrow m=1000\times 5.96\times 10^{-4}\\\Rightarrow m=0.596\ kg/s$

Heat is given by

$\frac{q}{t}=\frac{m}{t}S\Delta T\\\Rightarrow 30=0.596\times 4.186(T_f-10)\\\Rightarrow T_f=\frac{30}{0.596\times 4.186}+10\\\Rightarrow T_f=22.02\ ^{\circ}C$

The maximum possible temperature of the hot water that each showering resident receives is 22.02°C