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1 Chemistry and Physics Thermal Energy / Heat Study Guide Dr. Hazlett Thermochemistry and Thermodynamics I. Symbols and Conversion Equations A. Symbols Used: 1. t = Temperature 2. m = Mass 3. Cp = Specific Heat or Heat Capacity in J/goC 4. Q = Heat amount transferred in J or kJ 5. H = Enthalpy 6. S = Entropy 7. G = Gibbs Free Energy 8. W = Work 9. U = Internal Energy, also symbolized by E 10. M = Molar Mass 11. P = Pressure 12. V = Volume 13. ΔT = Change in Temperature (t2 – t1) B. Temperature Conversions 1. Tc = .556 x (Tf - 32) 2. Tf = (1.8 x Tc) + 32 3. Tk = Tc + 273.16 4. TR = Tf + 460 Celsius / Centigrade Fahrenheit Kelvin Rankine a. ΔTk = ΔTc C. Energy Conversions 1. 1 Calorie = 4.185 Joules (J) 2. 1 BTU = 1.055 x 103 J a. Energy needed to raise 1 lb H2O 1oF from 63 to 64 b. 1 BTU = 252 cal = 1056 J c. Convert cal/g to BTU/lb by multiplying cal/g by 1.8 3. 1 Joule = .2390 calorie 4. 1 kcal = 1 dietary calorie = 1000 calories (103 cal) a. Energy needed to raise 1 g H2O 1o C from 14.5 to 15.5 II. Temperature A. Kinetic Molecular Theory 1. Molecules absorbing energy increases KE, causing more random movements and collisions, increases level of thermal energy (heat) B. Temperature – measure of the average KE of the molecules of a substance, a measure of the intensity of energy in a system Chemistry and Physics Thermal Energy / Heat Study Guide Dr. Hazlett 2 C. Heat Transference: 1. Conduction – heat transferred from 1 particle to another w/o movement of matter itself a. H = K AΔt Δtime L where H is amount of heat flowing through a body with length L and cross section A; K is thermal conductivity; Δt is change in temp; and ΔT is change in time b. K is heat in kcal that will pass in 1 sec through a 1m3 with 2 opoosite sides w/ a 1oC difference in temperature c. R value (1) measure of thermal conductivity (2) Heat flow over time = thermal conductivity x area/length x ΔT (3) Thermal resistance = length / thermal conductivity 2. Convection – movement of heat via currents 3. Radiation – heat transferred by EM waves and/or particles a. Stefan-Boltzmann Law (1) E = kT4 (2) Energy (E) is radiated per second by a body w/ absolute temp (T) and k is proportionality constant (3) If E is in kcal radiated per m2/s, then k = 1.3567 x 10-11 kcal/m2sok4 or 5.67 x 10-8 J/m2sok4 (4) E = kT4AΔt 4. Other Information: a. Heat flows / moves in 1 direction until equilibrium acquired b. Heat always flows towards the cooler area c. Conductor carries heat / energy; insulators prevent it D. Specific Heat or Heat Capacity 1. Cp = _Q_ mΔT a. Measured in J/gCO or J/gK b. Amount of energy needed to raise the temp of the substance 1oC c. Ratio between thermal capacity of substance and the thermal capacity of water d. Greater the Cp, greater the heat needed to raise its temp 2. Q = CpmΔT; ΔT = Q/Cpm; m = Q/CpΔT; Q = nCpΔT (n is moles) 3. Calorimetry – measuring changes in thermal energy a. Conservation of thermal energy occurs between two objects b. EA + EB = Constant with ΔEA + ΔEB = 0 c. mACA(T2 - TA1) + mBCB(T2 - TB1) = 0 T2 = mACATA1 + mBCBTB1 mACA + mBCB 3 Chemistry and Physics Thermal Energy / Heat Study Guide Dr. Hazlett d. Heated object into cooler substance, vice versa: (1) QA = QB; m(ΔT)(Cp) = m(ΔT)(Cp) (2) Mass (m) = Volume x Density 4. Thermal Expansion a. Length L2 = L1 + α L1 (T2 – T1) or ΔL = αL1ΔT (1) Where α is linear coefficient of expansion based on material (2) α = ΔL L1ΔT b. Area ΔA = 2αΔT A1 c. Volume ΔV = 3αΔT V1 β = 3α ΔV = βVΔT III. Heat of Fusion / Vaporization A. Heat of Fusion – constants that show the amount of heat to change the state of any specified mass of material from a solid to liquid state w/o changing its temperature 1. Amount of energy needed to melt 1 kg of a substance (water is 80 cal/g) 2. HF = mLF where HF is heat needed; m is mass; and LF is heat of fusion a. Also symbolized as QF (1) QF = mHF b. In J/kg 3. Molar Heat of Fusion – amount of heat needed to melt one mole substance a. Q = ΔHfus(mass/molar mass) in kJ/mol (1) Water = 6.02 kJ/mol = 79.7 cal/ml = 334 J/g B. Heat of Vaporization – amount of heat needed to change any given mass of a material to a gaseous state (water is 540 cal/g) 1. Amount of energy needed to change 1 kg into a gas from liquid 2. Hv = mLv where LV is heat of vaporization a. Also symbolized as Qv (1) QV = mHv Molar Heat of Vaporization – to turn I mole into a vapor/liquid in kJ/mol 3. a. Q = ΔHvap(mass/molar mass) in kJ/mol (1) Water = 40.7 kJ/mol = 539 cal/ml = 2260 J/g IV. Thermodynamics / Thermochemistry A. 1st Law - the mechanical equivalent of heat, and in any process – the total amount of energy remains constant (Basically the Law of Conservation of Energy) 1. Thermal energy can be increased by adding heat or work to a system a. Total increase in themal energy of a system is the Σ W and added heat 2. W = mechanical equivalent of heat Q Chemistry and Physics Thermal Energy / Heat Study Guide Dr. Hazlett 4 B. 2nd Law – natural processes go in a direction that maintains/increases the total entropy of the universe (i.e. from hot to cold); every spontaneous change is accompanied by an increase in entropy (S and at STP is So) 1. Entropy (S) is the measure of randomness/disorder in a system; increases as heat increases a. Law of Disorder – spontaneous processes always proceed in such a way that entropy of the universe increases b. Predicting changes in entropy (1) ΔSsystem = Sproducts - Sreactants (a) Sproducts > Sreactants and ΔS is + (b) Sproducts < Sreactants and ΔS is – c. Change of Entropy Situations: (1) Can predict changes in entropy associated w/ changes in phases (2) Entropy increases w/ increase in KE (3) Dissolving gas in a solvent results in decrease in S (4) Increase in T causes an increase in S (5) If no change in phase, S of system increases when number of gaseous product particles is greater than the number of gaseous reactant particles (6) Heat cannot be converted completely into useful work (7) Every isolated system becomes disordered over time 4. Gibbs Free Energy (G) a. A combination of entropy and enthalpy (1) Tells how far rxn is from a state of equilibrium b. G of the system, or free energy, is the energy available to do work c. ΔGsystem is difference between ΔHsystem and the product of ΔoK temp and ΔSsystem (1) ΔGsystem = ΔHsystem - T ΔSsystem at STP (2) if change of G is neg, rxn is spontaneous C. 3rd Law – As temperature approaches absolute zero, the entropy of the system approaches a constant minimum D. Zeroth Law – if 2 thermodynamic systems are in equilibrium with a third, then they are in thermal equilibrium with each other E. Enthalpy (H) – the heat content of a system at constant pressure 1. ΔH or ΔHrxn is the change in heat of a reaction (endo/exothermic) a. ΔHrxn = Hfinal - Hinitial or ΔHrxn = Hproducts - Hreactants b. Exothermic rxn have negative enthalpy 2. H = E + PV or H = U + PV where E is internal energy, P is pressure and V is volume F. Thermochemical Equations 1. A balanced equation with all physical states of units included an the change of energy indicated (ΔH) a. ΔHo is standard enthalpy change at STP (1 atm and 25oC / 298K) b. Example: C6H12O6(s) + 6O2(g) 6CO2(g) + 6H2O(l) ΔHcomb = -2808kJ 5 Chemistry and Physics Thermal Energy / Heat Study Guide Dr. Hazlett 2. Molar Enthalpy of: a. Fusion (ΔHofus) is heat required to melt one mole of a solid (1) Water = 6.01 kJ b. Vaporization (ΔHovap) is heat needed vaporize one mole of a liquid (1) Water = 40.7 kJ 3. Calculating Enthalpy Change a. Uses a calorimeter to measure heat evolved / absorbed by reaction (1) For short time rxns b. Hess’s Law – Allows for total enthalpy of a rxn by breaking it down into a series of separate reactive steps (1) If can add 2+ thermochemical equations to produce a final equation for a rxn, then the sum of enthalpy changes for individual rxns is the enthalpy change for the final rxn 4. Reaction Spontaneity a. Spontaneous process is a physical/chemical change w/ no outside intervention (1) Exothermic are spontaneous; endothermic are not 5. Kapp’s Rule – method used to determine heat capacities for compound molecules in a liquid or solid phase at or near 293K a. Cp of l or s = to sum of Cp of the individual species in the cmpd multiplied by a constant determined by how many atoms of that element are in the compound b. Cp = Σ(aici) where a is individual components of compound and c its heat capacity 6. Newton’s Law of Cooling – the hotter an object is, the faster it cools a. Rate of cooling is proportional to the temp difference between an object and its surroundings b. T(t) = TA + (TH - TA)e –kt where TA is ambient temp, TH is initial temp of object, -k is constant and t is time c. H = A(THot - TCold) where A is area, H is heat loss, R is R insulating value d. H = AU(THot - TCold) where U is conductance V. General Information A. Water Data Cp ΔH (s) 2.108 J/goC Fusion (l) 4.187 J/goC Vaporization (g) 1.996 J/goC 6.02 kJ/mol 40.7 kJ/mol B. Example Using Water: Q = mCpΔT Q = mCpΔT Q = mLF Q = mCpΔT Q = mLV ______________________________________________________________ - xoC 0 oC 100oC +xoC Solid Liquid Vapor / Gas Σ Q = Q1 + Q2 + Q3 + Q4 + Q5 6 Chemistry and Physics Thermal Energy / Heat Study Guide Dr. Hazlett Specific heats and molar heat capacities for various substances at 20 C c in cal/gm K or Molar C Btu/lb F J/mol K Substance c in J/gm K Aluminum 0.900 0.215 24.3 Bismuth 0.123 0.0294 25.7 Copper 0.386 0.0923 24.5 Brass 0.380 0.092 ... Gold 0.126 0.0301 25.6 Lead 0.128 0.0305 26.4 Silver 0.233 0.0558 24.9 Tungsten 0.134 0.0321 24.8 Zinc 0.387 0.0925 25.2 Mercury 0.140 0.033 28.3 2.4 0.58 111 Water 4.186 1.00 75.2 Ice (-10 C) 2.05 0.49 36.9 Granite .790 0.19 ... Glass .84 0.20 ... Alcohol(ethyl) Specific Heat Capacities Table J/kg/oC or J/kg/K cal/g/oC or cal/g/K Methyl Alcohol 2549 0.609 Steam (100 oC) 2009 0.480 Benzene 1750 0.418 Wood (typical) 1674 0.400 Soil (typical) 1046 0.250 Air (50 C) 1046 0.250 Marble 858 0.205 Glass (typical) 837 0.200 Iron/Steel 452 0.108 Substance o 7 Chemistry and Physics Thermal Energy / Heat Study Guide Dr. Hazlett Melting Points and Heat of Fusion Substance Helium Melting point Melting point Heat of fusion K °C (103 J/kg) 3.5 -269.65 5.23 Hydrogen 13.84 -259.31 58.6 Nitrogen 63.18 -209.97 25.5 Oxygen 54.36 -218.79 13.8 Ethyl alcohol 159 -114 104.2 Mercury 234 -39 11.8 Water 273.15 0.00 334 Sulfur 392 119 38.1 Lead 600.5 327.3 24.5 Antimony 903.65 630.50 165 Silver 1233.95 960.80 88.3 Gold 1336.15 1063.00 64.5 1356 1083 134 Copper *From Young, Hugh D., University Physics, 7th Ed. Table 15-4. Boiling point K Boiling point °C Heat of vaporization (103 J/kg) Helium 4.216 -268.93 20.9 Hydrogen 20.26 -252.89 452 Nitrogen 77.34 -195.81 201 Oxygen 90.18 -182.97 213 Ethyl alcohol 351 78 854 Mercury 630 357 272 Water 373.15 100.00 2256 Sulfur 717.75 444.60 326 Lead 2023 1750 871 Antimony 1713 1440 561 Silver 2466 2193 2336 Gold 2933 2660 1578 Copper 2840 2567 5069 Boiling Points and Heat of Vaporization Substance *From Young, Hugh D., University Physics, 7th Ed. Table 15-4. 8 Chemistry and Physics Thermal Energy / Heat Study Guide Dr. Hazlett State Temperature K Hydrogen Triple point 13.81 Hydrogen Boiling point 20.28 Neon Boiling point 27.102 Oxygen Boiling point 54.361 Argon Triple point 83.798 Oxygen Boiling point 90.188 Water Triple point 273.16 Water Boiling point 373.125 Tin Melting point 505.074 Zinc Melting point 692.664 Silver Melting point 1235.08 Gold Melting point 1337.58 Temperature Standard Points Substance Primary fixed points in the international temperature scale. From Halliday and Resnick Triple Point Data Substance Temperature Pressure K 105Pa Helium-4 (-point) 2.17 0.0507 Hydrogen 13.84 0.0704 Deuterium 18.63 0.171 Neon 24.57 0.432 Oxygen 54.36 0.00152 Nitrogen 63.18 0.125 Ammonia 195.40 0.0607 Sulfur dioxide 197.68 0.00167 Carbon dioxide 216.55 5.17 Water 273.16 0.00610 From Young, University Physics, 8th Ed., Table 16-3