Re: [Phys-l] Work done on tyre

[carmelo@pacific.net.sg]

Quoting John Denker <jsd@av8n.com>:
> Is this a thermodynamics problem?  I'd say not, since it doesn't
> involve the second law.  For that matter, it doesn't really depend
> on the first law, either;  a high-school-physics notion of
>   work = force * distance
> suffices, doesn't it?
>
> What am I missing?  Is there a tricky trap here that makes this
> harder than it looks?  If so, I fell into the trap ... please
> explain.

Thanks for the responses from John, Jack, etc…
Actually, this question has many “traps”.
1. First “Trap”: Some students consider that there is no work done on  
fixed volume tyre.

Work done = p (deltaV) = 0 since the tyre does not expand.
(By the way, the rubber tyre may contract when heat is absorbed.)

2. Second “Trap”: Some apply First Law:
                  Delta U = Q + W
Assume there is no heat transfer, rubber tyre is a very good insulator, Q = 0

Work done = Delta U = 3RT/2 (n2 – n1)

3. Third “Trap”: Some carry out the integral of pdV.

Work done = Integral of pdV = nRT ln (V2 / V1)

4. Fourth “Trap”: One is concerned with the possibility of calculating  
the heat transfer. Could this be pseudowork? Could internal energy be  
considred differently...

U = E(kinetic) + E(interaction) + E(particle)
E(interaction) may refer to the potential energy depending on the  
relative coordinates of the particles, and may also depend on the  
different types of gases introduced into the tyre. Different gases in  
the tyre may have different “interaction” energies.
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Actually, i don't know the “correct” answer, but it is interesting  
that many students view the question differently. Perhaps, the one who  
set the question may have other insights too… By the way, a colleague  
just posed me this PhD qualifying Exam question: How many magnetic  
field lines are there in the universe? The answer is ONE!
Is this another fair question? Have Fun!


Best regards,
Alphonsus