## An electric motor drawing 10 amps at 110 V in steady state produces shaft power at 9.7 Nm and 1000 RPM. For a first Law analysis and conside

Question

An electric motor drawing 10 amps at 110 V in steady state produces shaft power at 9.7 Nm and 1000 RPM. For a first Law analysis and considering the motor as the control volume How much heat will be produced from the motor (in Watts)

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3 years 2021-08-17T06:45:36+00:00 1 Answers 7 views 0

The heat rate produced from the motor is 84.216 watts.

Explanation:

The electric motor receives power from electric current and releases power in the form of mechanical energy (torque) and waste heat and can be considered an stable-state system. The model based on the First Law of Thermodynamics for the electric motor is:

Where:

– Heat transfer from the electric motor, measured in watts.

– Electric power, measured in watts.

– Mechanical power, measured in watts.

The heat transfer rate can be calculated in terms of electric and mechanic powers, that is:

The electric and mechanic powers are represented by the following expressions:

Where:

– Current, measured in amperes.

– Steady-state voltage, measured in volts.

– Torque, measured in newton-meters.

– Angular speed, measured in radians per second.

Now, the previous expression for heat transfer rate is expanded:

The angular speed, measured in radians per second, can be obtained by using the following expression:

Where:

– Rotational rate of change, measured in revolutions per minute.

If , then:

Given that , , and , the heat transfer rate from the electric motor is:

The heat rate produced from the motor is 84.216 watts.