Question

The power to operate a heater comes from a 24-volt [V] power supply. The efficiency of the heater is 73%, and the heater produces 700 kilojoules of output heat per hour [kJ/h]. Determine the resistance of the heating element in units of ohms [Ω].

Answer 1

The heater resistance is 2.167 ohms.

Step-by-step explanation:

According to the First Law of Thermodynamics, electric work becomes heat transfer rate. From Ohm's Law and definition of efficiency we get that output heat rate (
`\dot Q_(out)`), measured in watts, is represented by:

`\dot Q_(out) = (\eta\cdot V^(2))/(R)` (Eq. 1)

Where:

`\eta` - Heating efficiency, dimensionless.

`V` - Power supply voltage, measured in volts.

`R` - Heater resistance, measured in ohms.

Now we clear the heater resistance:

`R = (\eta \cdot V^(2))/(\dot Q_(out))`

If we know that
`\dot Q_(out) = 194\,W`,
`\eta = 0.73` and
`V = 24\,V`, then the heater resistance is:

`R = ((0.73)\cdot (24\,V)^(2))/(194\,kW)`

`R = 2.167\,\Omega`

The heater resistance is 2.167 ohms.