Question

A 90-hp (shaft output) electric car is powered by an electric motor mounted in the engine compartment. If the motor has an average efficiency of 91 percent, determine the rate of heat supply by the motor to the engine compartment at full load.

Answer 1

Answer:

The rate of heat supply is 8.901 horse-power.

Explanation:

From Thermodynamics energy efficiency of the electric car ($\eta$), no unit, is the ratio of translational mechanical power ($\dot E_{out}$), measured in horse power, to electric power ($\dot E_{in}$), measured in horse-power. The rate of heat supply ($\dot E_{l}$), measured in horse-power, by the motor to the engine compartment at full load is difference between electric energy and translational mechanical energy. That is:

$\eta = \frac{\dot E_{out}}{\dot E_{in}}$ (1)

$\dot E_{l} = \dot E_{in}-\dot E_{out}$ (2)

$\dot E_{l} = \left(\frac{1}{\eta}-1\right)\cdot \dot E_{out}$ (3)

If we know that $\eta = 0.91$ and $\dot E_{out} = 90\,hp$, then rate of heat supply is:

$\dot E_{l} = \left(\frac{1}{0.91}-1 \right)\cdot (90\,hp)$

$\dot E_{l} = 8.901\,hp$

The rate of heat supply is 8.901 horse-power.