I was wondering if there is any way of theoretically determing properties of matter such as melting point, boiling point, coefficient of linear expansion, specific heat, etc. All these values are experimentally derived as far as i know. If there is no theoretical way of determining these values, what is the reason? Is it just far to complex to handle or is it because are current theories are not complete enough? Also, in order to determine this properities what would be required?
in order to determine these quantities, you need a theoretical model for the system whose properties you want to determine. for example, by treating a solid as a lattice of atoms that behave approximately like linear springs obeying hooke s law (F=-kx), you can calculate pretty accurately the specific heat. all you need to input is the strength of the spring, which is related to the strength of the coulomb interaction between atoms. so you only need to know the coulomb constant. in principle any of the quantities you mentioned can be calculated in this manner, although in practice it can become difficult for certain types of systems. in particular, metals, crystals, and gasses submit to these models rather well. perhaps you re familiar with the ideal gas law? PV=nRT. this was originally an experimental law, and the constant of relation, R, the ideal gas constant, was experimentally determined. but the law can also be derived theoretically using a rather simple model of treating the atoms as billard balls, so to speak. all these theoretical derivations were regarded as conclusive proof of the atomic model, which was still rather contraversial as late as the turn of the last century.
You can predict properties of matter with mathematical models. The calculations are very complex, so you basically have to have a computer to do it accurately. Our models aren't perfect, so while they can often give a very good approximation of how materials will behave it is usually best to actually test a real sample of the material to be sure. These sorts of calculations are often used for designing new materials. http://www.wavefun.com/ makes some really nice software for simulating things.
Of course there is a way, that is how scientists know some of the the properties of elements not yet discovered. This way, they know what to look for. However, the latest elements have all been man-made in a laboratory and have lasted only for a very short amount of time. Edited to add bold comment. Thank you RDT2.
You can predict some aspects of the macroscopic properties of materials (e.g elastic modulus) from a knowledge of microscopic properties (e.g bond stiffness). However, the prediction tends to be of the theoretical maximum for the property, i.e for a perfect material. Real materials always contain flaws which can drastically reduce the theoretical props - so it's always wise to do some experiments. Cheers, Ron T. http://www.mech.gla.ac.uk/~rthomson
More specifically I guess I am wondering about melting and boiling points of materials. I have looked at values for them on the periodic table and its all across the board. The values jump way up and down. This fascinates me a great deal. The thing is these values of melting, boiling, etc. are determined by the subatomic properties of the element. So could, say, quantum mechanics be used to find ut these values, its just that the calculations involved are beyond are current means of calculating? Related to that, wasnt there something about bohr's model of the hydrogen atom accuractely determining the spectrum lines for hydrogen. I dont remember it that clearly, but was it expanded to include spectrum lines for the other elements or can they still not do that? Anyways, I guess i would just like to see a nice neat unified theory for all these properties of matter. Like given the number of electrons and all being able to calculate the values of all these properties from one theory and one model. So does such a theory exist? Is quantum mechanics this theory? If so, is it just being limited by our ability to calculate the results? Michael
yes, in principle quantum mechanics is the theory. well, combined with statistical mechanics. quantum mechanics tells us the microscopic properties of the particles, and statistical mechanics tells us how to properly average the billions and billions of particles, since it is unreasonable to calculate the state of every single particle if all you re interested in is the bulk properties, like melting point, etc.. in principle, every bulk property is knowable this way. but in practice some things are harder to calculate than others. basically, it depends on how complicated the model you use is. a model usually involves some simplifying assumptions. if you simplify too much, the model doesn t describe reality very well. if your model is too complex, it will be very difficult to perform the calculations. and even if you do, you might be spending 90% of your effort calculating terms that only change your answer by 0.1%. part of doing good physics is deciding what simplifications are useful and efficient, and which are too strict. i m not sure where boiling and melting points fit into this scheme. i imagine that for some elements, it can be predicted pretty accurately, say for elements with only one valence electron. i dunno. for molecules with 10 atoms in them, it could be very difficult. a lot of this boils down to the fact that many-body problems are not exactly solvable. we know how the a single moon orbits a planet, but it is very difficult to calculate exactly how 3 bodies orbit each other. now imagine solving an iron atom, which has 56 electrons orbiting it. put it next to another iron atom with 56 electrons as well. how do the electrons of the single atom interact with each other? how do they interact with the adjacent atom? what does the net force look like? it turns out that for metals, it is a very good model to treat the valence electrons as a free electron gas, and ignore the bound electrons. but it s just a model. in principle, every electron interacts with every other electron in the universe. you have to assume that certain electrons (like those on jupiter, or those in the atomic subshell) do not interact. re: the bohr model. the bohr model is just false. but you ve got the right idea. for the reasons i described above, it is easy to do hydrogen, and hard to do multi-electron atoms. modern quantum mechanics can do much better than the bohr model for multi-electron atoms by making some simplifying assumptions, but the results are only approximate. to sum up: in principle, all the bulk properties are calculable. in practice, certain systems of equations are not exactly soluble. part of being a physicist is knowing how to force an approximate answer out of an insoluble equation.
