Heat capacity anomaly in the vicinity of the tricritical and upper critical points |
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Authors: | V P Voronov E E Gorodetskii A T Berestov |
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Institution: | (1) Institute of Oil and Gas Problems, Russian Academy of Sciences, Moscow, 119991, Russia;(2) Moscow State Institute of Electronic Engineering (Technical University), Zelenograd, Moscow oblast, 103498, Russia |
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Abstract: | The anomalous behavior of the isochoric heat capacity of a mixture of methane, pentane and heptane is studied experimentally in the vicinity of the liquid-vapor critical point in the cases when (a) the critical temperature T c approaches the tricritical point T TCP and (b) the critical temperature approaches the upper critical end point T U . It is shown that in all cases, the singular part of the heat capacity of the mixture has the form Csing=A¦τ¦?α, where τ=(T ? T c )/T c and α≈0.11. When T c →T U , amplitude A of the heat capacity anomaly is found to be approximately constant. At the same time, the amplitude of the anomaly tends to zero in the vicinity of the tricritical point: A∝¦τc¦ε, where τc=(T c ? T TCP )/T TCP and ε=1.6?1.7. The inevitable vanishing of this mode of the heat capacity anomaly leads to a negative value of the critical index \(\tilde \alpha\) characterizing the heat capacity anomaly at the tricritical point, while the tricritical point theory and the isomorphism hypothesis predict \(\tilde \alpha = 0.5\). |
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