Lecture note 12 (10-13-2011)

# Lecture note 12 (10-13-2011) - MAE 581 Advanced Materials...

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1 MAE 581 Advanced Materials Science Lecture note 12 Phase equilibrium and structure Stability of phases Every material in a given state has a characteristic heat content or enthalpy, H , and the rate of change of heat content with temperature is equal to the specific heat of the material measured at constant pressure, C P =(d H/ d T ) P . The knowledge of the quantity H is clearly important to understand reactions but it does not provide a criterion for equilibrium, nor does it determine when a phase change occurs, as shown by the occurrence of both exothermic and endothermic reactions. To provide this criterion it is necessary to consider a second important property of state known as the entropy, S . In statistical terms S may be regarded as a measure of the state of disorder of the structure, but from classical thermodynamics it may be shown that for any material passing through a complete cycle of events: where d Q is the heat exchanged between the system and its surroundings during each infinitesimal step and T is the temperature at which the transfer takes place. It is then convenient to define a quantity S such that d S =d Q/T , so that ; entropy so defined is then a state property. At constant pressure, d Q =d H and consequently which by integration gives

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2 where S is the entropy at T (K), usually measured in JK 1 . The integration constant S 0 represents the entropy at absolute zero, which for an ordered crystalline substance is taken to be zero; this is often quoted as the third law of thermodynamics. Clearly, any reaction or transformation within a
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## Lecture note 12 (10-13-2011) - MAE 581 Advanced Materials...

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