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Re: [Phys-l] entropy and electric motors



Hi John;

This is helpful. I guess I need to read the Nyquist paper (and I will) to see what the connection between Johnson noise and the second law.

So would it be fair to think of the thermal noise as roughly parallel to the Qout of a heat engine?

Do you happen to know where the loss comes from in real electric engines?

kyle

PS I am reading the digest version so I only get this once a day.


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Message: 11
Date: Thu, 22 May 2008 14:26:13 -0700
From: John Denker <jsd@av8n.com>
Subject: Re: [Phys-l] entropy and electric motors
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <4835E4F5.7080603@av8n.com>
Content-Type: text/plain; charset=us-ascii

On 05/22/2008 01:45 PM, kyle forinash wrote:
Does anyone know (or can point me to an explanation) of how the 2nd law
applies to electric motors and generators?

I think I understand how the 2nd law applies to heat engines and I have
an elementary understanding of entropy as it relates to chemical
reactions. These applications explain why heat engines and fuel cell
efficiencies cannot be 100%. I assume the 2nd law applies somehow to
motors and generators but how do you find the theoretical limit for
them? (I know this is quite high since electric motors with 95%
efficiency are already available.)

Here's a back-of-the envelope calculation that may illustrate
the principles involved.

Heat engines have a problem because "heat energy" by definition
has a lot of entropy per unit energy.

To a first approximation, commonly-available sources of electric
power have very little entropy per unit energy. Let's ask how
low the applied input voltage would have to be before it would
be thermodynamically impossible for the motor to consume power,
because it would be emitting just as much power backwards into
the supply as it was receiving. We can use the Johnson noise
formula
V^2 / R = 4 kT B
where B is the bandwidth, R is the resistance, and V is the RMS
noise voltage. This formula is a direct corollary of the 2nd
law, as Nyquist proved (in a paper published back-to-back with
Johnson's experimental paper). If we take R on the order of 1
ohm and B on the order of a few Hz, then V is a fraction of a
nanovolt.

Power goes like voltage squared.

The power ratio [(fractional nanovolt) / (115 V)]^2 is nonzero
"in principle" but it is commonly approximated as being zero.

Does that answer the question?



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--
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"When applied to material things,
the term "sustainable growth" is an oxymoron."
Albert Bartlett

kyle forinash 812-941-2039
kforinas@ius.edu
http://Physics.ius.edu/
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