DULONG PETIT LAW OF SPECIFIC HEAT College ppt (2)

DULONG PETIT LAW OF SPECIFIC HEAT College ppt (2)

1. PRESENTATION ON PRESENTED BY SHEETAL PANWAR PRESENTED TO MR. GYANRAO DHOTE DULONG PETIT’S LAW OF SPECIFIC HEAT

2. INTRODUCTION The Dulong–Petit law , a thermodynamic rule proposed in 1819 by French physicists Pierre Louis Dulong and Alexis Therese 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

3. IN MODERN TERMS 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

4. MODERN THEORY OF HEAT CAPACITY 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

5. 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 3 R / 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 . EQUIVALENT FORMS OF STATEMENT OF THE LAW

6. The initial form of the Dulong–Petit law was: cM = K            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 .             m/M = N   Therefore, using uppercase C for the total heat capacity, and lowercase c for the specific heat capacity c  : (C/m)M = K    C(M/m) = C/N = K = 3R                                                     or              . C/N = 3R Therefore the heat capacity of most solid crystalline substances is 3R per mole of substance

7. APPLICATION LIMITS Despite its simplicity, Dulong–Petit law offers fairly good prediction for the specific heat capacity of many elementary solids with relatively simple crystal structure at high temperatures. The Dulong–Petit law fails at room temperatures for light atoms bonded strongly to each other, such as in metallic beryllium, and in carbon as diamond. In the very low (cryogenic) temperature region, where the quantum mechanical nature of energy storage in all solids manifests itself with larger and larger effect, the law fails for all substances.