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I noticed that universal electric motors have peculiar electrical <=> mechanical transfer function, which seems to break the second law of thermodynamics.

Can anyone show where did I do the mistake ?

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Universal motor (series wounded) is a motor where rotor and stator currents always equal on magnitude.

The transfer function between mechanical and electrical domains is (ideally):

T = k*I^2,

which can be expressed also by:

U/I = k*w.

(T = torque, w = angular velocity, I = current, U = voltage, k = motor constant)

This says that a motor rotating clockwise (in this example, k>0) can act as a motor only (the sign of the torque equals to the sign of angular velocity), and not as a generator.

And the same motor rotating counter-clockwise can act as a generator only (the sign of torque differs from the sign of angular velocity), and not as a motor.

Now we take a very small universal motor rotating clockwise (k>0), and connect the terminals to a resistor; and we heat up the whole system to high (and uniform) temperature. Any electrical thermal noise presented in the electrical system (resistor, cables, coils) is seen as fluctuating AC-current in the circuit. And if this noise-current has any effect on rotation, it can only increase the angular velocity.

Also any mechanical noise on rotor (AC component of w) cannot change the sign of U*I ( =sign(U/I) ) as long as w>0, which is the requirement for transferring mechanical energy to electrical domain; so mechanical noise energy can not be transferred to electrical noise energy.

So for me it looks like any thermal energy in the resistor is transferred to thermal electrical noise which is then transferred to mechanical energy.

Another way to see is that the noise temperature of hot universal motor approaches zero Kelvins, thus breaking the second law of thermodynamics.

And this is not restricted to rotating machines only (requiring sparky/noisy commutators).

Another kind of universal motor is a plain wire loop. Any current, not depending on the sign of it, on the loop creates a magnetic field which tries to maximize the area of the loop. In any moment, the force on small part of wire is k*I^2 (k might vary during loop expansion), which classifies this as a universal motor.

I definitely missed something, but cannot pinpoint it.

BR, -Topi

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# Universal motor and the second law of thermodynamics

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