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

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

Step-by-step 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

Answer 2

`\dot m = 0.047 kg/s`

Step-by-step 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 = (W)/(c_p *(T_(OUT) - T_(IN)))`
`= (11)/(4.18 *(70-15))`

`\dot m = 0.047 kg/s`