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In Equilibrium thermodynamics by C.J Adkins he mentions an example about degrees of freedom of a thermodynamic system --

Very often for a simple system it is possible to say immediately that how many degrees of freedom it has from a knowledge of it's properties .For example , a wire subject to tension only has 2 degrees of freedom ,for it is known that it's length depends on tension and temperature only

So I don't really understand that how he concludes that the wire has only two degrees of freedom only by knowledge of the fact that it's length depends only on tension and temperature..

Because for me there are many more thermodynamic properties of this system apart from it's length...so how can we conclude it.

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  • $\begingroup$ Can you name another property that is of relevance to the length of the wire? $\endgroup$
    – lemon
    Apr 2, 2016 at 10:01
  • $\begingroup$ @lemon are you sayin that all other properties so far are totally dependent on length and temperature $\endgroup$ Apr 2, 2016 at 10:29
  • $\begingroup$ In thermodynamics, you want to look at relavant degrees of freedom subject to the problem you are posed or you want to solve. Resistance could be a degree of freedom, but how can it be related tension applied on the wire. It would therefore be useful to consider when solving electrical circuit problems to use resistance as a degree of freedom with temperature. $\endgroup$
    – user35952
    Apr 2, 2016 at 10:33
  • $\begingroup$ You have it the wrong way round, @HiteshPathak. It's not that all other properties are dependent on tension and temperature, it's that the length is dependent only on tension and temperature. $\endgroup$
    – lemon
    Apr 2, 2016 at 10:38
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    $\begingroup$ Yes, so the minimum number of properties required is only 2, tension and length (of course temperature is there, but then you have an equation of state as a constraint) to describe the mechanical properties of the wire from thermodynamics, like expansivity etc. Now if you want extract some other properties of wire, then you will use a different set of parameters with a different equation of state. $\endgroup$
    – user35952
    Apr 2, 2016 at 11:03

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The minimum number of properties required is only 2, tension and length (of course temperature is there, but then you have an equation of state as a constraint) to describe the mechanical properties of the wire from thermodynamics, like expansivity etc. There would be other mechanical parameters (pressure, volume etc.) but would have very little effect on the properties in the case of the wire.

Now if you want extract some other properties of wire (non mechanical), then you will use a different set of parameters with a different equation of state. For example, if your interested calculating some electrical properties of the wire using thermodynamics (like resistivity for instance), then you have to choose parameters that are relevant that physical situation with a different equation of state.

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