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Unformatted text preview: et al., Nature, 410 , 653-654) uses such an equation of state to analyze the mechanical response of “the hardest known oxide.” In this problem, you will derive a simple relationship between the internal energy and the volume of a system. Define the bulk modulus as: B = − V ∂ P ∂ V ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ T Now, consider the experimental observation that the derivative of the bulk modulus is a function of pressure. This allows us to approximate the bulk modulus as B ( P ) = B + B 1 P . For the purposes of this problem, consider the case where the free energy does not depend on the entropy, ∂ U ∂ S ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ V = Using these two thermodynamic observations, develop an expression for the free energy, U ( V ) , in terms of the parameters B and B 1 , and the volume at zero pressure, V ....
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This note was uploaded on 02/12/2011 for the course E 115 taught by Professor Staff during the Fall '08 term at University of California, Berkeley.
- Fall '08