Energy Balance

Upon studying this section, you should be familiar with the following:

In this section, we began with specific definitions for types of energies, such as the one for kinetic energy. Then, we went on to perform energy balances on closed, open, and mechanical systems. From there we ended up with systems where ΔH = Q. For these cases, we found ΔH's for temperature, pressure, and state changes, as well as for reactions. Summing all these up gave us the ΔH around the reactor. In a list format, these are the interrelations that you need from the energy balances covered in this course.

  • 3 forms of energy with the equations for:
    Ek, ΔEk, (as well as Ė k and ΔĖk),
    Ep, ΔEp, (as well as Ė p and ΔĖp),
    U related to Cv
    H related to Cp
    U related to H
    Cp to Cv

  • understand specific properties, those per some quantity of mass or mole, such as , Ĥ, etc.
  • The closed system energy balance
  • The open system energy balance
  • Mechanical system energy balance (and what assumptions are made to turn it into the Bernoulli equation)
  • hat
  • When are ΔEk, ΔEp, ΔU, ΔH, Q, W, and Ws equal to zero? (Hint: no change in velocity, height, temperature, {temperature (and pressure if not an ideal gas)}, adiabatic or insulated, no work of shaft and no flow (nor electrical, etc.), no shaft work, respectively)
  • Suddenly, many terms vanish, and we end up dealing with, ΔH = Q
  • To determine ΔH for the following:
    • for a change in pressure, for an ideal gas = 0, for a solid or liquid, = Vhat * ΔP
    • for a change in temperature, ΔH = ò Cp dT, from Tinitial to Tfinal
    • for a change in state, just look up the value (careful with the signs, ΔĤv = -ΔĤcondensation, etc)
    • Don't forget, there is a psychrometric chart for air-water systems, these charts take into account changes in state, such as condensation, and changes in temperature, for the entire air-water system!!
    • for a reaction, find ΔĤreaction using Hess's Law or Heats of Formation, or if applicatable, from tabulated ΔH's for combustion reactions
      and get x and other unknown flow rates from material balances, to give ΔHrxn
    • And, of course, to remember we need to get the phase changing species to the tabulated phase change temperature, and for chemical reactions, we need to get all species involved to STP conditions!!

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