Tuesday, March 26, 2013

Clausius-Clapeyron Equation

The Clausius-Clapeyron Equation shows the relationship between temperature and saturation vapor pressure, which determines when water substance changes phase. It allows the calculation of the vapor pressure at another temperature. The Clausius-Clapeyron Equation works because the vaporization curves of most liquids have similar shapes. The Clausius-Clapeyron Equation is dP/dT=L/T(delta times v), where dP/dT is the slope of tangent to the coexistence curve at any point, L is the latent heat, T is the temperature, and delta times v is is the volume change of the phase transition (see below). The equation has different forms depending on what it is applied to (see below). The Clausius-Clapeyron Equation is named after Rudolf Clausius (1822-1888) and Benoit Paul Emile Clapeyron (1799-1864).

\frac{\mathrm{d}P}{\mathrm{d}T} = \frac{L}{T\,\Delta v},
The Clausius-Clapeyron Equation

\frac{\mathrm{d}e_s}{\mathrm{d}T} = \frac{L_v(T) e_s}{R_v T^2}
The Clausius-Clapeyron Equation Applied to Meteorology
\ln P = -\frac{L}{R}\left(\frac{1}{T}\right)+C.
The Clausius-Clapeyron Equation Applied to Chemistry

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