Question

A) Cold water at 15 °C flows in at the rate of 0.0036 m3 / minute. Hot water flows out at the same rate.

Calculate the mass of water that passes the heating element in one minute.

The density of water is 1000 kg / m3

b) The power of the heating element is 8.5 kW.

Calculate the temperature of the hot water that flows out.

The specific heat capacity of water is 4200 J /(kg °C)

Answer 1

Given:-

Initial temperature, $T_{i}=15^{0}C$

Flow rate of water, $Q=0.0036m^{3}/min$

Density of water, $\rho=1000kg/m^{3}$

Power, P=8.5 kW=8500W

Specific heat of water, $C_{p}=4200J/kg-K$

To Find:-

mass of water and final temperature of water.

Explanation:-

$\text{mass flow rate of water, }\dot{m}=\text{density}(\rho)\times\text{discharge(Q)}\\\\\Rightarrow\dot{m}=1000\times0.0036=3.6kg/min=0.06kg/s\\\\\text{Now, }\\\\\text{Power, }P=\dot{m}\times C_{p}\times(T_{f}-T_{i})\text{ where,}\\\\T_{f}=\text{Final temperature of water}\\\\\Rightarrow8500=0.06\times4200\times(T_{f}-15)\Rightarrow T_{f}=48.73^{0}C\\\\\text{Therefore, final temperature of hot water that flows out is }48.73^{0}C$