The Birch–Murnaghan isothermal equation of state, published in 1947 by Albert Francis Birch of Harvard, [1] is a relationship between the volume of a body and the pressure to which it is subjected. Birch proposed this equation based on the work of Francis Dominic Murnaghan of Johns Hopkins University published in 1944, [2] so that the equation is named in honor of both scientists.
Expressions for the equation of state
The third-order Birch–Murnaghan isothermal equation of state is given by
![{\displaystyle P(V)={\frac {3B_{0}}{2}}\left[\left({\frac {V_{0}}{V}}\right)^{7/3}-\left({\frac {V_{0}}{V}}\right)^{5/3}\right]\left\{1+{\frac {3}{4}}\left(B_{0}^{\prime }-4\right)\left[\left({\frac {V_{0}}{V}}\right)^{2/3}-1\right]\right\}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/67f7c0792f4179a6d15b7639f2f6a6cd3901c917)
![{\displaystyle f={\frac {1}{2}}\left[\left({\frac {V_{0}}{V}}\right)^{2/3}-1\right]\,,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/68c8c73eaac6e0584db4a2aaeb4214dd81950190)
The internal energy, E(V), is found by integration of the pressure:
![{\displaystyle E(V)=E_{0}+{\frac {9V_{0}B_{0}}{16}}\left\{\left[\left({\frac {V_{0}}{V}}\right)^{2/3}-1\right]^{3}B_{0}^{\prime }+\left[\left({\frac {V_{0}}{V}}\right)^{2/3}-1\right]^{2}\left[6-4\left({\frac {V_{0}}{V}}\right)^{2/3}\right]\right\}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0db7e4a3022c1d3abb6e3ed4cfb895ec3038c5f)
See also
References
- ^ Birch, Francis (1947). "Finite Elastic Strain of Cubic Crystals". Physical Review. 71 (11): 809–824. Bibcode: 1947PhRv...71..809B. doi: 10.1103/PhysRev.71.809.
- ^ Murnaghan, F. D. (1944). "The Compressibility of Media under Extreme Pressures". Proceedings of the National Academy of Sciences of the United States of America. 30 (9): 244–247. Bibcode: 1944PNAS...30..244M. doi: 10.1073/pnas.30.9.244. JSTOR 87468. PMC 1078704. PMID 16588651.
- ^ a b Poirier, J.-P. (2000). "Introduction to the Physics of the Earth's Interior". Cambridge. ISBN 9781139164467.
| Theory |  | |
|---|---|---|
| Statistical thermodynamics | ||
| Models | ||
| Mathematical approaches | ||
| Critical phenomena | ||
| Entropy | ||
| Applications | ||
 | This classical mechanics–related article is a stub. You can help Wikipedia by expanding it. |
 | This article about statistical mechanics is a stub. You can help Wikipedia by expanding it. |
The Birch–Murnaghan isothermal equation of state, published in 1947 by Albert Francis Birch of Harvard, [1] is a relationship between the volume of a body and the pressure to which it is subjected. Birch proposed this equation based on the work of Francis Dominic Murnaghan of Johns Hopkins University published in 1944, [2] so that the equation is named in honor of both scientists.
Expressions for the equation of state
The third-order Birch–Murnaghan isothermal equation of state is given by
The internal energy, E(V), is found by integration of the pressure:
See also
References
- ^ Birch, Francis (1947). "Finite Elastic Strain of Cubic Crystals". Physical Review. 71 (11): 809–824. Bibcode: 1947PhRv...71..809B. doi: 10.1103/PhysRev.71.809.
- ^ Murnaghan, F. D. (1944). "The Compressibility of Media under Extreme Pressures". Proceedings of the National Academy of Sciences of the United States of America. 30 (9): 244–247. Bibcode: 1944PNAS...30..244M. doi: 10.1073/pnas.30.9.244. JSTOR 87468. PMC 1078704. PMID 16588651.
- ^ a b Poirier, J.-P. (2000). "Introduction to the Physics of the Earth's Interior". Cambridge. ISBN 9781139164467.
| Theory | | |
|---|---|---|
| Statistical thermodynamics | ||
| Models | ||
| Mathematical approaches | ||
| Critical phenomena | ||
| Entropy | ||
| Applications | ||
|
| This classical mechanics–related article is a stub. You can help Wikipedia by expanding it. |
|
| This article about statistical mechanics is a stub. You can help Wikipedia by expanding it. |