Physics, 18.07.2020 04:01, steffweikeloyrt00

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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answered: libertycooper

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:

$\dot W_{e} - \dot W_{T} -\dot Q = 0$

Where:

$\dot Q$ - Heat transfer from the electric motor, measured in watts.

$\dot W_{e}$ - Electric power, measured in watts.

$\dot W_{T}$ - Mechanical power, measured in watts.

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

$\dot Q = \dot W_{e} - \dot W_{T}$

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

$\dot W_{e} = i \cdot V$

$\dot W_{T} = T \cdot \omega$

Where:

- Current, measured in amperes.

- Steady-state voltage, measured in volts.

- Torque, measured in newton-meters.

$\omega$ - Angular speed, measured in radians per second.

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

$\dot Q = i \cdot V - T \cdot \omega$

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

$\omega = \frac{\pi}{30}\cdot \dot n$

Where:

$\dot n$ - Rotational rate of change, measured in revolutions per minute.

If $\dot n = 1000\,rpm$ , then:

$\omega = \left(\frac{\pi}{30} \right)\cdot (1000\,rpm)$

$\omega \approx 104.720\,\frac{rad}{s}$

Given that $i = 10\,A$ , $V = 110\,V$ , $T = 9.7\,N\cdot m$ and $\omega \approx 104.720\,\frac{rad}{s}$ , the heat transfer rate from the electric motor is:

$\dot Q = (10\,A)\cdot (110\,V) -(9.7\,N\cdot m)\cdot \left(104.720\,\frac{rad}{s} \right)$

$\dot Q = 84.216\,W$

The heat rate produced from the motor is 84.216 watts.

answered: Guest

second mirror gathers light from a faraway object and reflects it to another mirror. - a.

answered: Guest

elly's long hair:

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justin can't pay the full balance:

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