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Birch–Murnaghan equation of stateIn continuum mechanics, an equation of state suitable for modeling solids is naturally rather different from the ideal gas law. A solid has a certain equilibrium volume V_{0}, and the energy increases quadratically as volume is increased or decreased a small amount from that value. The simplest plausible dependence of energy on volume would be a harmonic solid, with Additional recommended knowledgeThe next simplest reasonable model would be with a constant bulk modulus Murnaghan equation of stateA more sophisticated equation of state was derived by Francis D. Murnaghan of Johns Hopkins University in 1944 . To begin with, we consider the pressureand the bulk modulus Experimentally, the bulk modulus pressure derivative is found to change little with pressure. If we take B' = B'_{0} to be a constant, then
where B_{0} is the value of B when P = 0. We may equate this with (2) and rearrange as Integrating this results in or equivalently Substituting (6) into then results in the equation of state for energy. Many substances have a fairly constant B'_{0} of about 3.5. Birch–Murnaghan equation of stateThe thirdorder Birch–Murnaghan isothermal equation of state, published in 1947 by Francis Birch of Harvard , is given by:Again, E(V) is found by integration of the pressure: References

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Birch–Murnaghan_equation_of_state". A list of authors is available in Wikipedia. 