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T Use Maxwell relations to express the derivatives ᎧᏙ . capacities, the expansion coefficient a, and the isothermal compressibility KT. You may need to use the chain relation, the reciprocal relation, and the "path" relation and af af af ().-)...). + ду as P in terms of heat

T Use Maxwell relations to express the derivatives ᎧᏙ . capacities, the expansion coefficient a, and the isothermal compressibility KT. You may need to use the chain relation, the reciprocal relation, and the "path" relation and af af af ().-)...). + ду as P in terms of heat

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Use Maxwell relations to express the derivatives \(\left( \frac{\partial S}{\partial V} \right)_T\) and \(\left( \frac{\partial V}{\partial S} \right)_P\) in terms of heat capacities, the expansion coefficient \(\alpha\), and the isothermal compressibility \(\kappa_T\). You may need to use the chain relation, the reciprocal relation, and the "path" relation \[ \left( \frac{\partial f}{\partial x} \right)_z = \left( \frac{\partial f}{\partial x} \right)_y + \left( \frac{\partial f}{\partial y} \right)_x \left( \frac{\partial y}{\partial x} \right)_z \]
Transcribed Image Text:Use Maxwell relations to express the derivatives \(\left( \frac{\partial S}{\partial V} \right)_T\) and \(\left( \frac{\partial V}{\partial S} \right)_P\) in terms of heat capacities, the expansion coefficient \(\alpha\), and the isothermal compressibility \(\kappa_T\). You may need to use the chain relation, the reciprocal relation, and the "path" relation \[ \left( \frac{\partial f}{\partial x} \right)_z = \left( \frac{\partial f}{\partial x} \right)_y + \left( \frac{\partial f}{\partial y} \right)_x \left( \frac{\partial y}{\partial x} \right)_z \]
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