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The Dulong–Petit law, a thermodynamic rule proposed in 1819 by French physicists Pierre Louis Dulong and Alexis Thérèse Petit, states the classical expression for the molar specific heat capacity of certain chemical elements. Experimentally the two scientists had found that the heat capacity per weight (the mass-specific heat capacity) for a number of elements was close to a constant value, ''after'' it had been multiplied by a number representing the presumed relative atomic weight of the element. These atomic weights had shortly before been suggested by Dalton. In modern terms, Dulong and Petit found that the heat capacity of a mole of many solid elements is about 3''R'', where ''R'' is the modern constant called the universal gas constant. Dulong and Petit were unaware of the relationship with ''R'', since this constant had not yet been defined from the later kinetic theory of gases. The value of 3''R'' is about 25 joules per kelvin, and Dulong and Petit essentially found that this was the heat capacity of certain solid elements, per mole of atoms they contained. The modern theory of the heat capacity of solids states that it is due to lattice vibrations in the solid, and was first derived in crude form from this assumption by Albert Einstein, in 1907. The Einstein solid model thus gave for the first time a reason why the Dulong–Petit law should be stated in terms of the classical heat capacities for gases. ==Equivalent forms of statement of the law== An equivalent statement of the Dulong–Petit law in modern terms is that, regardless of the nature of the substance, the specific heat capacity c of a solid element (measured in joule per kelvin per kilogram) is equal to 3R/''M'', where ''R'' is the gas constant (measured in joule per kelvin per mole) and ''M'' is the molar mass (measured in kilogram per mole). Thus, the heat capacity per mole of many elements is 3''R''. The initial form of the Dulong–Petit law was: : where c is the specific heat, ''M'' the atomic weights accepted in that day, and K is a new constant which we know today is about 3R. In modern terms the mass m divided by atomic weight ''M'' gives the number of moles N. : Therefore, using uppercase C for the ''total'' heat capacity, and lowercase c for the specific heat capacity c : : : or :. Therefore the heat capacity of most solid crystalline substances is 3R per mole of substance. Dulong and Petit did not state their law in terms of the gas constant ''R'' (which was not then known). Instead, they measured the values of heat capacities (per weight) of substances and found them smaller for substances of greater atomic weight as inferred by Dalton and other early atomists. Dulong and Petit then found that when multiplied by these atomic weights, the value for the heat capacity (which would now be the heat capacity ''per mole'' in modern terms) was nearly constant, and equal to a value which was later recognized to be 3 ''R''. In other modern terminology, the dimensionless heat capacity is equal to 3. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dulong–Petit law」の詳細全文を読む スポンサード リンク
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