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Explain why the coefficient of thermal expansion for a solid vanishes at T=0.

Explain why the coefficient of thermal expansion for a solid vanishes at T=0.

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The Third Law of Thermodynamics gathers several important observations on the behavior of systems at very low temperature into a single general rule. The observations include the following 1. The most striking outcome of low-temperature experiments is the failure to achieve the absolute zero of temperature. While low-temperature physicists are constantly setting new records for minimum temperature, each order-of-magnitude decrease has required a commensurably greater experimental effort. The results suggest that temperature asymptotes toward zero without actually reaching it. This conclusion is not inconsistent with the Second Law since the requirement that T not be negative is satisfied if T only exists in the open interval T>0 2. The values of the thermodynamic properties of real materials show a surprising uniformity as temperature approaches zero. The specific heats of all known substances vanish as T0 to an order that is at least linear in T; the specific heat of a metal is propor- tional to T near T = 0 while that of an insulator or semiconductor is proportional to T. The coefficient of thermal expansion of a solid and the variation of its pressure with temperature vanish as T0 along with a number of other material properties. In fact, if q and p are a geometric coordinate and its conjugate force, it is always found that op 0q 0T where the subscripts indicate that the partial derivatives are taken with q and p, respectively, held constant. 3. All known substances seek minimum-entropy states as the temperature ap- proaches zero. Fluid phases condense into crystalline solids and solid solutions order or decompose into ordered phases page 67 Notes on the Thermodynamics of Solids J.W Momis, Jr: Fall, 2008 4. The entropy changes in standard chemical reactions vanish as T0 as do the entropy differences between different crystalline modifications of the same substance. The entropy differences between the simple states of pure components and other states that have frozen-in degrees of freedom, such as a crystal and a glass of the same substance, do not vanish as T0, but tend toward small, constant values. In many cases these small differ ences can be calculated from statistical thermodynamics, and prove to be just the difference in configurational entropy These results can all be derived as consequences of a single postulate regarding the behavior of the entropy as T0

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