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

Answer:

The heater resistance is 2.167 ohms.

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:

$\dot Q_{out} = \frac{\eta\cdot V^{2}}{R}$ (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:

$R = \frac{\eta \cdot V^{2}}{\dot Q_{out}}$

If we know that $\dot Q_{out} = 194\,W$, $\eta = 0.73$ and $V = 24\,V$, then the heater resistance is:

$R = \frac{(0.73)\cdot (24\,V)^{2}}{194\,kW}$

$R = 2.167\,\Omega$

The heater resistance is 2.167 ohms.