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Energy

Energy. Thermodynamics Professor Lee Carkner Lecture 3. PAL # 2 Pressure. Use barometer to find height of Empire State Building Convert mm of Hg into Pa using P = r gh P top = (13600)(9.8)(0.730) = P bottom = (13600)(9.8)(0.763) =

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Energy

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  1. Energy Thermodynamics Professor Lee Carkner Lecture 3

  2. PAL # 2 Pressure • Use barometer to find height of Empire State Building • Convert mm of Hg into Pa using P = rgh • Ptop = (13600)(9.8)(0.730) = • Pbottom = (13600)(9.8)(0.763) = • Difference in pressure between top and bottom is equal to the pressure of a column of air the height of the building • DP = rgh = 4398.24 Pa = (1.2)(9.8)h • h =

  3. PAL # 2 Pressure • Assumptions: • Constant g • Other ways to find height: • drop off top

  4. Energy • If we consider the energy in a certain region all we need to know is net input and output • e.g. a refrigerator heats up your kitchen but keeps your food cold • Why? • Not all the forms are equally useful

  5. Total Energy • Energy is a useful analytical tool because it is a conserved, scalar quantity • Total energy is E (extensive property), total energy per unit mass is e = E/m (intensive property) • Fix zero at some useful point

  6. Scale of Energy • We want to sort energy out by usefulness • Macroscopic energy is possessed by the whole system • Organized and useful • Microscopic energy is possessed by the individual particles • Disorganized and not very useful

  7. Organized and Disorganized Energy

  8. Internal Energy • Many different kinds of microscopic energy • Some internal energies are related to motion and kinetic energy and are known as the sensible energy • Generally proportional to temperature

  9. Types of Internal Energy

  10. Non-Sensible Energies • Latent energy • Can be released with phase change • Chemical energy • Can be released by chemical reactions (e.g. burning) • Nuclear energy • Can be released in fusion or fission reactions

  11. Sum of Energies • The total energy is the sum of three things • The kinetic energy = ½mv2 • Total energy per unit mass • Stationary fluids don’t change ke or pe and so the equation reduces to e = u

  12. Mechanical Energy • Mechanical energy can be converted completely to mechanical work • Key engineering systems that rely on mechanical energy are pumps and turbines • Flow work

  13. Energy of Flow emech = (P/r)+(v2/2)+gz • If the fluid is flowing then the total energy rate (E’) is just the energy per unit mass times the mass flow rate (m’) • m’ is in kg/s

  14. Change in Energy • The energy of the fluid depends only on its pressure, velocity and height • We can then write: • DE’mech = m’[(DP/r)+(D(V2)/2)+g(Dz)] • Sign depends on signs of the deltas • Negative is power needed to input (pump)

  15. Heat • Heat is the energy transferred due to a temperature difference • Heat is only heat while it is being transferred • It has thermal energy

  16. A Potato

  17. Heat Transfer • Heat is designated by Q (or q for heat per unit mass) • Heat is transferred in three ways: • Conduction: • Convection: • Radiation: • While all objects in the universe emit and absorb heat, only objects at different temperatures have a net heat transfer

  18. Work • Work can be expressed as: • work per unit mass: w • Sign convention: • Negative: work in, heat out • Note that work and heat are not state functions, they are associated with a process

  19. Path Functions • We represent the quantity to be integrated over the path with an inexact differential, dW • Thus the total work is: • The total work is the sum of all the small differential works (dW) done along the way

  20. Mechanical Work • Generally speaking the work differential can be written: • For each type of system we need to find how the force varies with displacement • In these cases the work is the sum of the changes in kinetic and potential energy

  21. Linear Displacement • A boundary is moved in 1, 2 or 3 dimensions • Spring work (1D): • W = ∫ F dx = ½k(x22-x21) • Stretched Film (2D): • W = ∫ ss dA • Hydrostatic (3D): • W = ∫ P dV

  22. Spring Work

  23. Stretched Film

  24. Shaft Work • The displacement term is the circumference times the number of revolutions W = ∫ F ds = Fs = (T/r)(2prn) = 2pnT • The power is then: • Where n’ is revolutions per second

  25. Shaft

  26. Non-Mechanical Work • Non-mechanical work generally involves microscopic motion • Electrical work • Polarization work • Magnetic Work

  27. Next Time • Read: 2.6-2.7 • Homework: Chapter 2, P: 37, 46, 57, 63

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