Enthalpy of fusion - wikipedia Enthalpy of fusion For the plastic welding technique, see Heat fusion. Enthalpies of melting and boiling for pure elements versus temperatures of transition, demonstrating Trouton 's rule. The enthalpy of fusion of a substance, also known as ( latent ) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid, ( or resulting from the release of energy from a substance during transition from liquid to solid ), at constant pressure. ( It is used to decribe the change in phase of matter of melting or freezing ). This energy includes the contribution required to make room for any associated change in volume by displacing its environment against ambient pressure. The temperature at which the phase transition occurs is the melting point or the freezing point, according to context. By convention, the pressure is assumed to be 1 atm ( 101.325 kPa ) unless otherwise specified. Contents 1 Overview 2 Examples 3 Solubility prediction 3.1 Proof 4 See also 5 Notes 6 References Overview The ' enthalpy ' of fusion is a latent heat, because during melting the heat energy needed to change the substance from solid to liquid at atmospheric pressure is latent heat of fusion, as the temperature remains constant during the process. The latent heat of fusion is the enthalpy change of any amount of substance when it melts. When the heat of fusion is referenced to a unit of mass, it is usually called the specific heat of fusion, while the molar heat of fusion refers to the enthalpy change per amount of substance in moles. The liquid phase has a higher internal energy than the solid phase. This means energy must be supplied to a solid in order to melt it and energy is released from a liquid when it freezes, because the molecules in the liquid experience weaker intermolecular forces and so have a higher potential energy ( a kind of bond - dissociation energy for intermolecular forces ). When liquid water is cooled, its temperature falls steadily until it drops just below the line of freezing point at 0 ° C. The temperature then remains constant at the freezing point while the water crystallizes. Once the water is completely frozen, its temperature continues to fall. The enthalpy of fusion is almost always a positive quantity ; helium is the only known exception. Helium - 3 has a negative enthalpy of fusion at temperatures below 0.3 K. Helium - 4 also has a very slightly negative enthalpy of fusion below 0.77 K ( − 272.380 ° C ). This means that, at appropriate constant pressures, these substances freeze with the addition of heat. In the case of He, this pressure range is between 24.992 and 25.00 atm ( 2,533 kPa ). Standard enthalpy change of fusion of period three. Standard enthalpy change of fusion of period two of the periodic table of elements. Substance Heat of fusion ( cal / g ) Heat of fusion ( J / g ) water 79.72 333.55 methane 13.96 58.99 propane 19.11 79.96 glycerol 47.95 200.62 formic acid 66.05 276.35 acetic acid 45.90 192.09 acetone 23.42 97.99 benzene 30.45 127.40 myristic acid 47.49 198.70 palmitic acid 39.18 163.93 sodium acetate 63 -- 69 264 -- 289 stearic acid 47.54 198.91 gallium 19.2 80.4 Paraffin wax ( C H ) 47.8 - 52.6 200 -- 220 These values are mostly from the CRC Handbook of Chemistry and Physics, 62nd edition. The conversion between cal / g and J / g in the above table uses the thermochemical calorie ( cal ) = 4.184 joules rather than the International Steam Table calorie ( cal ) = 4.1868 joules. Examples A ) To heat 1 kg ( 1.00 liter ) of water from 283.15 K to 303.15 K ( 10 ° C to 30 ° C ) requires 83.6 kJ. However, to melt ice also requires energy. We can treat these two processes independently ; thus, to heat 1 kg of ice from 273.15 K to water at 293.15 K ( 0 ° C to 20 ° C ) requires : ( 1 ) 333.55 J / g ( heat of fusion of ice ) = 333.55 kJ / kg = 333.55 kJ for 1 kg of ice to melt PLUS ( 2 ) 4.18 J / ( g K ) × 20K = 4.18 kJ / ( kg K ) × 20K = 83.6 kJ for 1 kg of water to increase in temperature by 20 K = 417.15 kJ From these figures it can be seen that one part ice at 0 ° C will cool almost exactly 4 parts water from 20 ° C to 0 ° C. B) Silicon has a heat of fusion of 50.21 kJ / mol. 50 kW of power can supply the energy required to melt about 100 kg of silicon in one hour, after it is brought to the melting point temperature : 50 kW = 50 kJ / s = 180 000 kJ / h 180 000 kJ / h * ( 1 mol Si ) / 50.21 kJ * 28 gSi / ( mol Si ) * 1kgSi / 1000gSi = 100.4 kg / h Solubility prediction The heat of fusion can also be used to predict solubility for solids in liquids. Provided an ideal solution is obtained the mole fraction ( x 2 ) ( displaystyle ( x_ ( 2 ) ) ) of solute at saturation is a function of the heat of fusion, the melting point of the solid ( T f u s ) ( displaystyle ( T_ ( mathit ( fus ) ) ) ) and the temperature ( T ) of the solution : ln ⁡ x 2 = − Δ H f u s ∘ R ( 1 T − 1 T f u s ) ( displaystyle ln x_ ( 2 ) = - ( \frac ( Delta H_ ( mathit ( fus ) ) ^ ( circ ) ) ( R ) ) left ( ( \frac ( 1 ) ( T ) ) - ( \frac ( 1 ) ( T_ ( mathit ( fus ) ) ) ) \right ) ) Here, R is the gas constant. For example, the solubility of paracetamol in water at 298 K is predicted to be : x 2 = exp ⁡ ( − 28100 J mol − 1 8.314 JK − 1 mol − 1 ( 1 298 − 1 442 ) ) = 0.0248 ( displaystyle x_ ( 2 ) = exp ( left ( - ( \frac ( 28100 ( mbox ( J mol ) ) ^ ( - 1 ) ) ( 8.314 ( mbox ( JK ) ) ^ ( - 1 ) ( mbox ( mol ) ) ^ ( - 1 ) ) ) left ( ( \frac ( 1 ) ( 298 ) ) - ( \frac ( 1 ) ( 442 ) ) \right ) \right ) ) = 0.0248 ) This equals to a solubility in grams per liter of : 0.0248 ∗ 1000 g 18.053 mol − 1 1 − 0.0248 ∗ 151.17 mol − 1 = 213.4 ( displaystyle ( \frac ( 0.0248 * ( \frac ( 1000 ( mbox ( g ) ) ) ( 18.053 ( mbox ( mol ) ) ^ ( - 1 ) ) ) ) ( 1 - 0.0248 ) ) * 151.17 ( mbox ( mol ) ) ^ ( - 1 ) = 213.4 ) which is a deviation from the real solubility ( 240 g / L ) of 11 %. This error can be reduced when an additional heat capacity parameter is taken into account. Proof At equilibrium the chemical potentials for the pure solvent and pure solid are identical : μ s o l i d ∘ = μ s o l u t i o n ∘ ( displaystyle mu _ ( solid ) ^ ( circ ) = mu _ ( solution ) ^ ( circ ) , ) or μ s o l i d ∘ = μ l i q u i d ∘ + R T ln ⁡ X 2 ( displaystyle mu _ ( solid ) ^ ( circ ) = mu _ ( liquid ) ^ ( circ ) + RT ln X_ ( 2 ) , ) with R ( displaystyle R , ) the gas constant and T ( displaystyle T , ) the temperature. Rearranging gives : R T ln ⁡ X 2 = − ( μ l i q u i d ∘ − μ s o l i d ∘ ) ( displaystyle RT ln X_ ( 2 ) = - ( mu _ ( liquid ) ^ ( circ ) - mu _ ( solid ) ^ ( circ ) ) , ) and since Δ G f u s ∘ = μ l i q u i d ∘ − μ s o l i d ∘ ( displaystyle Delta G_ ( mathit ( fus ) ) ^ ( circ ) = mu _ ( liquid ) ^ ( circ ) - mu _ ( solid ) ^ ( circ ) , ) the heat of fusion being the difference in chemical potential between the pure liquid and the pure solid, it follows that R T ln ⁡ X 2 = − ( Δ G f u s ∘ ) ( displaystyle RT ln X_ ( 2 ) = - ( Delta G_ ( mathit ( fus ) ) ^ ( circ ) ) , ) Application of the Gibbs -- Helmholtz equation : ( ∂ ( Δ G f u s ∘ T ) ∂ T ) p = − Δ H f u s ∘ T 2 ( displaystyle left ( ( \frac ( partial ( ( \frac ( Delta G_ ( mathit ( fus ) ) ^ ( circ ) ) ( T ) ) ) ) ( partial T ) ) \right ) _ ( p , ) = - ( \frac ( Delta H_ ( mathit ( fus ) ) ^ ( circ ) ) ( T ^ ( 2 ) ) ) ) ultimately gives : ( ∂ ( ln ⁡ X 2 ) ∂ T ) = Δ H f u s ∘ R T 2 ( displaystyle left ( ( \frac ( partial ( ln X_ ( 2 ) ) ) ( partial T ) ) \right ) = ( \frac ( Delta H_ ( mathit ( fus ) ) ^ ( circ ) ) ( RT ^ ( 2 ) ) ) ) or : ∂ ln ⁡ X 2 = Δ H f u s ∘ R T 2 ∗ δ T ( displaystyle partial ln X_ ( 2 ) = ( \frac ( Delta H_ ( mathit ( fus ) ) ^ ( circ ) ) ( RT ^ ( 2 ) ) ) * delta T ) and with integration : ∫ X 2 = 1 X 2 = x 2 δ ln ⁡ X 2 = ln ⁡ x 2 = ∫ T f u s T Δ H f u s ∘ R T 2 ∗ Δ T ( displaystyle int _ ( X_ ( 2 ) = 1 ) ^ ( X_ ( 2 ) = x_ ( 2 ) ) delta ln X_ ( 2 ) = ln x_ ( 2 ) = int _ ( T_ ( mathit ( fus ) ) ) ^ ( T ) ( \frac ( Delta H_ ( mathit ( fus ) ) ^ ( circ ) ) ( RT ^ ( 2 ) ) ) * Delta T ) the end result is obtained : ln ⁡ x 2 = − Δ H f u s ∘ R ( 1 T − 1 T f u s ) ( displaystyle ln x_ ( 2 ) = - ( \frac ( Delta H_ ( mathit ( fus ) ) ^ ( circ ) ) ( R ) ) left ( ( \frac ( 1 ) ( T ) ) - ( \frac ( 1 ) ( T_ ( mathit ( fus ) ) ) ) \right ) ) See also Heat of vaporization Heat capacity Thermodynamic databases for pure substances Joback method ( Estimation of the heat of fusion from molecular structure ) Latent heat Notes Jump up ^ Atkins & Jones 2008, p. 236. Jump up ^ Ott & Boerio - Goates 2000, pp. 92 -- 93. Jump up ^ Hoffer, J.K. ; Gardner, W.R. ; Waterfield, C.G. ; Phillips, N.E. ( April 1976 ). `` Thermodynamic properties of He. II. The bcc phase and the P-T and VT phase diagrams below 2 K ''. Journal of Low Temperature Physics. 23 ( 1 ) : 63 -- 102. Bibcode : 1976JLTP... 23... 63H. doi : 10.1007 / BF00117245. Jump up ^ Ibrahim Dincer and Marc A. Rosen. Thermal Energy Storage : Systems and Applications, page 155 Jump up ^ Measurement and Prediction of Solubility of Paracetamol in Water - Isopropanol Solution. Part 2. Prediction H. Hojjati and S. Rohani Org. Process Res. Dev. ; 2006 ; 10 ( 6 ) pp 1110 -- 1118 ; ( Article ) doi : 10.1021 / op060074g References Atkins, Peter ; Jones, Loretta ( 2008 ), Chemical Principles : The Quest for Insight ( 4th ed. ), W.H. Freeman and Company, p. 236, ISBN 0 - 7167 - 7355 - 4 Ott, BJ. Bevan ; Boerio - Goates, Juliana ( 2000 ), Chemical Thermodynamics : Advanced Applications, Academic Press, ISBN 0 - 12 - 530985 - 6 States of matter ( list ) State Solid Liquid Gas / Vapor Plasma Low energy Bose -- Einstein condensate Fermionic condensate Degenerate matter Quantum Hall Rydberg matter Strange matter Superfluid Supersolid Photonic matter High energy QCD matter Lattice QCD Quark -- gluon plasma Supercritical fluid Other states Colloid Glass Liquid crystal Quantum spin liquid Magnetically ordered Antiferromagnet Ferrimagnet Ferromagnet String - net liquid Superglass Transitions Boiling Boiling point Condensation Critical line Critical point Crystallization Deposition Evaporation Flash evaporation Freezing Chemical ionization Ionization Lambda point Melting Melting point Recombination Regelation Saturated fluid Sublimation Supercooling Triple point Vaporization Vitrification Quantities Enthalpy of fusion Enthalpy of sublimation Enthalpy of vaporization Latent heat Latent internal energy Trouton 's ratio Volatility Concepts Binodal Compressed fluid Cooling curve Equation of state Leidenfrost effect Macroscopic quantum phenomena Mpemba effect Order and disorder ( physics ) Spinodal Superconductivity Superheated vapor Superheating Thermo - dielectric effect Retrieved from `` https://en.wikipedia.org/w/index.php?title=Enthalpy_of_fusion&oldid=821116735 '' Categories : Thermodynamic properties Talk Contents About Wikipedia Afrikaans Aragonés Asturianu বাংলা Български Bosanski Català Čeština Dansk Deutsch Eesti Español Euskara فارسی Français Galego 한국어 Հայերեն Hrvatski Interlingua Italiano ქართული Қазақша Lietuvių La. lojban. 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Question: the heat required to change 1 gram of a solid at its normal melting point
Answer: The enthalpy of fusion of a substance, also known as (latent) heat of fusion