and the isothermal compressibility, kt = —

v the coefficient of thermal expansion, i ( dv

— I of substances, dp Jt can be measured. Using these parameters and since thermodynamic properties are mathematically well-behaved functions, namely the order of differentiation does not make any difference, i.e., can be measured. Using these parameters and since thermodynamic properties are mathematically well-behaved functions, namely the order of differentiation does not make any difference, i.e.,

fdz y |
f di |
'dZ y" | ||

_ dX |
_ drl |
M J_ |

the elimination of the non-measurable properties becomes simple.

In general, the Maxwell relations are obtained from {dZ=M dX + N dY}

the elimination of the non-measurable properties becomes simple.

In general, the Maxwell relations are obtained from {dZ=M dX + N dY}

V dV, paring this equation to the Gibbs' equation, {dU=T dS - p dV}, it is seen that v

| dU| = T and ( ■dU| =-p . Additionally, using the above property, we can

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