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Physics
Classical Physics
Thermodynamics
Change in Entropy of a Solid or Liquid
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[QUOTE="Chestermiller, post: 6194594, member: 345636"] For a single phase pure substance or a constant composition mixture, the variation in entropy can be determined from $$dS=\frac{C_p}{T}dT+\left(\frac{\partial S}{\partial P}\right)_TdP$$It follows from the equation $$dG=-SdT+VdP$$ that the partial derivative of entropy with respect to pressure is given by:$$\left(\frac{\partial S}{\partial P}\right)_T=-\left(\frac{\partial V}{\partial T}\right)_P$$ For a liquid or solid, the equation of state is $$dV=V(\alpha dT-\beta dP)$$where ##\alpha## is the volumetric coefficient of thermal expansion and ##\beta## is the bulk compressibility. So, $$\left(\frac{\partial V}{\partial T}\right)_P=\alpha V$$So, we have:$$dS=\frac{C_p}{T}dT-\alpha VdP$$ Because the specific volume and coefficient of thermal expansion of solids and liquids are very small, in virtually all practical situations, the second term is negligible. [/QUOTE]
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Physics
Classical Physics
Thermodynamics
Change in Entropy of a Solid or Liquid
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