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 ([tex]\dot Q_{out}[/tex]), measured in watts, is represented by:
[tex]\dot Q_{out} = \frac{\eta\cdot V^{2}}{R}[/tex] (Eq. 1)
Where:
[tex]\eta[/tex] - Heating efficiency, dimensionless.
[tex]V[/tex] - Power supply voltage, measured in volts.
[tex]R[/tex] - Heater resistance, measured in ohms.
Now we clear the heater resistance:
[tex]R = \frac{\eta \cdot V^{2}}{\dot Q_{out}}[/tex]
If we know that [tex]\dot Q_{out} = 194\,W[/tex], [tex]\eta = 0.73[/tex] and [tex]V = 24\,V[/tex], then the heater resistance is:
[tex]R = \frac{(0.73)\cdot (24\,V)^{2}}{194\,kW}[/tex]
[tex]R = 2.167\,\Omega[/tex]
The heater resistance is 2.167 ohms.
