| Clausius-clapeyron Relation |
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| CATEGORIES ABOUT CLAUSIUS-CLAPEYRON RELATION | |
| thermodynamics | |
| atmospheric thermodynamics | |
| chemical engineering | |
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: where ''dP''/''dT'' is the slope of the coexistence curve, ''L'' is the Latent Heat , ''T'' is the Temperature , and is the Volume . DERIVATION Suppose two phases, I and II, are in contact and at equillibrium with each other. Then the chemical potentials are related by μI = μII. Along the coexistence curve, we also have dμI = dμII. We now use the Gibbs-Duhem relation , where s and v are, respectively, the entropy and volume per particle, to obtain : Hence, rearranging, we have : From the relation between heat and change of entropy in a reversible process δQ=T dS, we have that the quantity of heat added in the transformation is : Combining the last two equations we obtain the standard relation. APPLICATION This equation can be used to work out whether or not a phase transition will occur. For example, the Clausius-Clapeyron relation is often invoked to explain Ice Skating : the increased pressure of the skater on the skates causes the ice to melt. Does this explanation work? If ''T'' = −2 °C, we can use the Clausius-Clapeyron relation to work out how much pressure is needed to melt ice. We can assume : and substituting in
and : = 2K, we get : = 27.2 MPa. This is an equivalent pressure to a Sumo Wrestler (mass = 150 kg) standing on a Stiletto Heel (area = 0.5 cm2)! Evidently, this is not how ice skating works. |
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