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Equations of state are thermodynamic relations which relate these \
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Later in 3.020, you will define various thermodynamic relations (Maxwell\
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In stable materials, pressure decreases with increased volume and thus the \
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If the bulk modulus becomes negative, then a decrease in volume would be \
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We require that the molar volume exhibits an inflection point\
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This amounts to the first and second derivatives (w.r.t. molar volume) vanish\
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We can express the van der Waals equation of state at the critical point as:\
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In this form, the equation can be solved for any of the critical variables in \
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Regions of positive slope identify where the system is mechanically unstable\
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Let\[CloseCurlyQuote]s visualize this unstable region by plotting where the \
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