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

22.02°C

Step-by-step explanation:

P = Power output = 30 kW

Volume flow rate of water =
`1.49* 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* 1.49* 10^(-4)\\\Rightarrow v=5.96* 10^(-4)\ m^3/s`

Mass flow rate is

`m=\rho* v\\\Rightarrow m=1000* 5.96* 10^(-4)\\\Rightarrow m=0.596\ kg/s`

Heat is given by

`(q)/(t)=(m)/(t)S\Delta T\\\Rightarrow 30=0.596* 4.186(T_f-10)\\\Rightarrow T_f=(30)/(0.596* 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