Question

Water is heated in an insulated, constant diameter tube by a 11-kW electric resistance heater. If the water enters the heater steadily at 15°C and leaves at 70°C, determine the mass flow rate of the water. Consider the specific heat of water at room temperature is cp = 4.18 kJ/kg·°C.

Answer 1

Answer:

$\dot m = 0.047 kg/s$

Explanation:

we know  by energy balanced for steady flow system that control volume W is given as

$W = \dot m c_p( T_{OUT} - T_{IN})$

here

$\dot m$ is mass flow rate

we have W = 11 kW

Outer temperature = 70°C

Inner temperature = 15°C

therefore we have mass flow rate

$\dot m = \frac{W}{c_p *(T_{OUT} - T_{IN})}$$= \frac{11}{4.18 *(70-15)}$

$\dot m = 0.047 kg/s$

Answer 2

Answer:

The mass flow rate of water is 0.0478 kg/s or 47.8 g/s

Explanation:

We have:

Power of electric heater = P = 11 KW

Change in temperature of water = ΔT = 70°C - 15°C = 55°C

Specific heat of water = C = 4.18 KJ / kg.°C

Now, from conservation of energy, we know that:

Energy dissipated by heater = Energy acquired by Water

Energy dissipated by heater = m C ΔT

Dividing both sides by time (t), we get:

Power of Heater = (mass flow rate) C ΔT

Mass Flow Rate = P/CΔT

Mass Flow Rate = (11 KW)/(4.18 KJ/kg.°C)(55°C)

Mass Flow Rate = 0.0478 kg/s = 47.8 g/s