The formulas of Ehrenfest are general formulas making it possible to calculate the Latent heat L of a transformation according to molar volumes of the body in the two phases with balance and knowing the curve of phase shift giving the pressure according to the temperature.

These formulas are:

$\backslash \; left\; (\backslash \; frac\; \{dp\}\; \{dT\}\; \backslash \; right)\; \_\; \{sat\}\; =\; \backslash \; frac\; \{\backslash \; alpha\_1\; -\; \backslash \; alpha\_2\}\; \{\backslash \; chi\_\; \{T,\; 1\}\; -\; \backslash \; chi\_\; \{T,\; 2\}\}\; ~$

$\backslash \; left\; (\backslash \; frac\; \{dp\}\; \{dT\}\; \backslash \; right)\; \_\; \{sat\}\; =\; \backslash \; frac\; \{c\_\; \{p,\; 1\}\; -\; c\_\; \{p,\; 2\}\}\; \{TV\; (\backslash \; alpha\_1\; -\; \backslash \; alpha\_2)\}\; ~$

This formula is valid in the case of a Transition from phase of the second order.

(For the transitions from first order phase to see the Formula of Clapeyron)

• $T\; ~$ Temperature to which the phase shift occurs.
• $v\; ~$ molar Volume common to both phases with balance.
• $\backslash \; alpha\_1,\; \backslash \; alpha\_2\; ~$ isobar Dilation coefficient respective of the two phases.
• $\backslash \; chi\_\; \{T,\; 1\},\; \backslash \; chi\_\; \{T,\; 2\}\; ~$ isothermal Compressibility respective of the two phases.
• $c\_\; \{p,\; 1\},\; c\_\; \{p,\; 2\}\; ~$ mass Heat capacity respective of the two phases
• $\backslash \; left\; (\backslash \; frac\; \{dp\}\; \{dT\}\; \backslash \; right)\; \_\; \{sat\}\; ~$ derived from the pressure compared to the temperature on the curve giving the pressure according to the temperature when the two phases coexist and are in balance.

Category: Thermodynamics