Now let s apply the heat stuff to real-world stuff like phase changes and the energy or cost it takes to carry it out. A heating curve...a plot of temperature of a substance vs heat added to a substance. Temperature C Heat Added (Joules)
Here s the same curve now applying the conservation of energy (sum of the heats) q = s ice m ice Tq = m ice H fus q = s H2 O m H2 O T q = m H2 O H vap q = s stm m stm T 220 Phase transition Temperature does not change during a phase transition. Phase transition Temperature does not change during a phase transition. F Steam Temperature C 100 0-100 Heating solid ice to 0 C A Ice B Ice + Water mix C Melting solid ice to 0 C water Water Heating water to boiling 100 C D Water + steam mix Boiling all water to steam 100 C E Heating steam past 100 C 4.12 38 79.3 305 309 Heat Added (kj/mole)
Calculate the amount of heat required to convert 500 grams of ice at -20.0 C to steam at 120. C. The specific heat capacities of water, ice and water vapor are 4.18, 2.06 and 1.84 J/g C respectively, and the latent heat of fusion and vaporization, ΔHf and ΔHv, are 6.02 and 40.7 kj/mol respectively. n i=1 q i = 0 sum the q s baby q = si mi ΔT for heating non-phase transitions qsolid=>liquid = (# moles) ΔH fusion for phase transitions qliquid=>gas = (# moles) ΔH vaporization
Calculate the amount of heat required to convert 500 grams of ice at -20 C to steam at 120 C. The specific heat capacities of water, ice and water vapor are 4.18, 2.06 and 1.84 J/g C respectively, and the latent heat of fusion and vaporization, ΔHf and ΔHv, are 6.02 and 40.7 kj/mol respectively. 1. Heat ice from -20 C to ice at 0 C = 500. g x 2.06 J/g C x 20 C 2. Melt ice at 0 C to water at 0 C = 500. g/(18 g/mol) x 6.02 kj/mol 3. Heat water from 0 C to water at 100 C= 500. g x 4.18 J/g C x 100 C 4. Evap water at 100 C to vap at 100 C = 500. g/(18 g/mol) x 40.7 kj/mol 5. Heat vap from 100 C to vap at 120 C = 500. g x 1.84 J/g C x 20 C 1. = 20.6 kj 2. = 167.2 kj 3. = 209.0 kj 4. = 1130.5 kj 5. = 18.4 kj Total = 1545.6 kj
Bunker fuel C, coal and rice hulls are the most widely used fuels in the Philippines (world too) used in create steam in nearly all industries worldwide. Look up the heating value of each of these fuels. By hook or by crook find the price per liter or price per kg of each of these fuels. Which fuel is the cheapest fuel to produce steam? What is the approximate cost to produce a MT steam at 120 C starting from 24 C assuming the efficiencies of all the heating processes are the same, and the cost of boilers are the same as well? Unfortunately not everything is simple economics. What other factors might one consider with each of these fuels assuming 15MT of steam is produced per day 7 days a week, 30 days a month and 12 months a year?
The concept of vapor pressure The equilibrium vapor pressure is the pressure exerted by a vapor over its liquid phase (measured under vacuum) when dynamic equilibrium exists between condensation and evaporation. Evaporation Vapor Pressure Liquid In open containers, molecules that have enough KE can overcome IMF s at the surface and evaporate into the atmosphere. Liquid In closed containers, molecules vaporize and condense until there is no further change in concentration in each phase. This forms an equilibrium vapor pressure over the liquid.
Dynamic chemical equilibrium is reached when there is no net change in the number of molecules: the rate of evaporation and the rate of condensation are equal. Molecules in liquid begin to vaporize Molecules vaporizing and condensing at such a rate that no net change in numbers occure
Dynamic equilibria is also reached in melting and sublimation and also in most chemical reactions. At the melting point a solid begins to change into a liquid as heat is added. As long no heat is added or removed melting (red arrows) and freezing (black arrows) occur at the same rate an the number of particles in the solid remains constant. aa + bb Reactants cc + dd Products Reaction Rate of the forward reaction = = Rate of Reverse reaction
Because kinetic energy (of molecules in any phase) depends on temperature, so does vapor pressure of a liquid. KE = Ek = 3 2 RT Relates molecular properties of molecules to bulk properties that we observe! Kinetic Energy Temperature More molecules escape at high temp At higher temperatures, a larger fraction of molecules have enough KE to escape the liquid phase.
The vapor pressure of a pure liquid (bulk property) depends on the intermolecular forces between molecules. The stronger the attractive forces in the liquid phase the lower the vapor pressure--and the less volatile it is. 2 atm Which of the following has the highest vapor pressure at 1 atm? Which is the least volatile at 1 atm?.66 atm water boils at 75 C at 300 torr =.4 atm
Vapor Pressure of Some Liquids
The following diagram shows a close-up view of part of the vapor-pressure curves for a solvent (red curve) and a solution of the solvent with a second liquid (green curve). Which solvent is more volatile?
The boiling point of a pure liquid is the temperature at which the equilibrium vapor pressure of a liquid over its liquid phase is equal to the external pressure on the liquid. The normal boiling point is the temperature at which a liquid boils when the external pressure is 1 atm. Evaporation Boiling
If we plot vapor pressure vs temperature we observe a linear relationship between ln P and 1/T. Vapor pressure plotted as a function of temperature ln (vapor pressure) plotted as a function of 1/Temp
The Clausius-Claperyron equation relates the vapor pressure (P) of a pure liquid to the liquid s temperature (T) and the liquids molar heat of vaporization ( H vap ). ln P = -ΔHvap R 1 + C T slope = H vap /R y = m x + b (note R = 8.31 J/K mol) ln P By taking measurements at two temps, we get: ln P 2 = -ΔHvap P R 1 1 1 T 2 T 1 1/T
Vapor pressure of pure etoh is 115 torr at 34.9 C. If ΔHvap = 40.5 kj/mol calculate the temperature when the vapor pressure of etoh is 760 torr. R is the gas constant given at 8.314 J/mol K