Purpose of doing Legendre Transform

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The Legendre transform is used in thermodynamics to switch from internal energy (U) as a function of entropy (S) to Helmholtz free energy (F) as a function of temperature (T), facilitating calculations. The transform simplifies analysis by allowing the use of temperature, which is easier to measure than entropy. Although the resulting equation F = U - TS still contains entropy, it provides a more practical framework for understanding thermodynamic systems. This approach helps in deriving other important thermodynamic relationships and properties. Ultimately, the Legendre transform enhances the ability to work with thermodynamic variables effectively.
cainjm3
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Hi, I'm new here, I was just wondering if anyone could help clarify a subject I'm having difficulties teaching myself... In thermo we perform a "Legendre transform" on the internal energy with respect to entropy. The stated purpose of this is so that we don't have to work in the entropy variable, since it is difficult to measure entropy. But the result of the transform (F = U - TS) still has entropy (S) in it. So how is this helpful? Thanks!
 
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