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Unformatted text preview: 5.6. SOME CONSERVATION AND EVOLUTION EQUATIONS 195 If one defines the net energy change of the reaction as U N summationdisplay i =1 i u i , (5.428) one then gets dT dt = r U c v . (5.429) The rate of temperature change is dependent on the absolute energies, not the energy dif ferences. If the reaction is going forward, so r &gt; 0, and that is a direction in which the net molar energy change is negative, then the temperature will rise. 5.6.4 Energy conservation: adiabatic, isobaric reaction Solving for the reaction dynamics in an adiabatic isobaric system requires some nonobvious manipulations. First, the first law of thermodynamics says dU = dQ dW . Since the process is adiabatic, one has dQ = 0, so dU + PdV = 0. Since it is isobaric, one gets d ( U + PV ) = 0, or dH = 0. So the total enthalpy is constant. Then d dt H = 0 , (5.430) d dt ( mh ) = 0 , (5.431) dh dt = 0 , (5.432) d dt parenleftBigg N summationdisplay i =1 c i h i parenrightBigg = 0 , (5.433) N summationdisplay...
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 Fall '11
 ParkSou
 Dynamics, Thermodynamics, Enthalpy, Energy, Entropy, Trigraph

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