Order of phase transitions
First-order phase transitions
Consider two phases , α and β, in equilibrium. Most phase transitions involve changes in enthalpy and in volume. These changes figure into the differences in the slope of the chemical potential curve on either side of the transition point.
In words, the difference in the slope of chemical potential versus pressure is simply the difference in the molar volumes of the two phases.The difference in the slopes of the chemical potential versus temperature is the difference in entropy or the difference in enthalpy over temperature for the transition in question. The slope is different on either side of the transition point. It is discontinuous at the transition.
This is a first-order phase transition. Remember that at the transition point, we are changing the enthalpy of the system but not its temperature. Thus, the heat capacity Cp at the transition point is infinite. In other words, as we heat the system that is at the transition point, no temperature change happens because all the heat is going into the phase transition.
Fig. 4.16 (from Atkins) The changes in thermodynamic properties accompanying (a) first-order and (b) second-order phase transitions.
Second-order Phase transitions
In a second-order phase transition, the first derivative of the slope of m is not discontinuous but it's second derivative is. In other words, there is an inflection point at the phase transition. This type of transitions occurs between conducting and superconducting phases of metals at low temperatures.
These transitions are not first order yet their heat capacity goes to infinity at the transition point. We saw such a transition between the two different liquid phases of helium at very low temperature. These transitions tend to include order/disorder transitions, paramagnet/ferromagnetic transitions and the fluid/superfluid transition of He.
Fig. 4.17 (Atkins) The λ-curve for helium, where the heat capacity rises to infinity. The shape of this curve is the origin of the name λ-transition.
รบกวนคนเก่งภาษาอังกฤษช่วยแปลให้หน่อยค่ะ ขอบคุณคะ
First-order phase transitions
Consider two phases , α and β, in equilibrium. Most phase transitions involve changes in enthalpy and in volume. These changes figure into the differences in the slope of the chemical potential curve on either side of the transition point.
In words, the difference in the slope of chemical potential versus pressure is simply the difference in the molar volumes of the two phases.The difference in the slopes of the chemical potential versus temperature is the difference in entropy or the difference in enthalpy over temperature for the transition in question. The slope is different on either side of the transition point. It is discontinuous at the transition.
This is a first-order phase transition. Remember that at the transition point, we are changing the enthalpy of the system but not its temperature. Thus, the heat capacity Cp at the transition point is infinite. In other words, as we heat the system that is at the transition point, no temperature change happens because all the heat is going into the phase transition.
Fig. 4.16 (from Atkins) The changes in thermodynamic properties accompanying (a) first-order and (b) second-order phase transitions.
Second-order Phase transitions
In a second-order phase transition, the first derivative of the slope of m is not discontinuous but it's second derivative is. In other words, there is an inflection point at the phase transition. This type of transitions occurs between conducting and superconducting phases of metals at low temperatures.
These transitions are not first order yet their heat capacity goes to infinity at the transition point. We saw such a transition between the two different liquid phases of helium at very low temperature. These transitions tend to include order/disorder transitions, paramagnet/ferromagnetic transitions and the fluid/superfluid transition of He.
Fig. 4.17 (Atkins) The λ-curve for helium, where the heat capacity rises to infinity. The shape of this curve is the origin of the name λ-transition.