First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. 438 0 obj
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The order of a phase transition is defined to be the order of the lowest-order derivative, which changes discontinuously at the phase boundary. 521 0 obj
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Physics 127b: Statistical Mechanics Lecture 3: First Order Phase Transitions The van der Waals equation for a gas is h PC a V2 i [V−b] DNkBT: (1)(The variable ais proportional to N2 and bto N, i.e. We shall discuss first-order transition in the next section. 402 0 obj
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6.2 First-order phase transition When water starts boiling, it undergoes a phase transition from a liquid to a gas phase. For both phases independently, the equation of state is a well-defined regular function, continuous, with continuous derivatives. ����g���sg��j[��FW6���; �b`��H+ �6H�Q������ conducting-superconducting transition in metals at low temperatures. These transitions are, e.g., characterized by changes in enthalpy or specific volume. First-order and second-order phase transitions (II) G Ttrs ΔGtrs 0 Second-order phase transition T V Ttrs T S Ttrs T H Cp-S T G P V P G T -continuous (S and V do not jump at transition) Ttrs T Ttrs T Strs 0 Htrs 0 P P dT dH C e.g. %%EOF
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h�b```���\M� cc`a�x�;����L{E�v���U�e�d�>8���a�� )/�d�x��왜^!K�v ,r@�����r����U�P���UJ�:��lY��$�T6�Z|�4m[�:�80"�)�T��EV�4&�1y|�U�J���$4n%� It can be motivated by rewriting it in the form Most phase transitions involve changes in enthalpy and in volume. A first order phase transition in the thresholdθ≥2 contact process on random r-regular graphs and r-trees Shirshendu Chatterjeea, Rick Durrettb,∗ a Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, United States