Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Mechanical energy
Document related concepts
no text concepts found
Transcript
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 = 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 = PAL # 2 Pressure Assumptions: Constant g Other ways to find height: drop off top 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 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 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 Organized and Disorganized Energy 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 Types of Internal Energy 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 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 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 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 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) Heat Heat is the energy transferred due to a temperature difference Heat is only heat while it is being transferred It has thermal energy A Potato 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 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 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 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 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 Spring Work Stretched Film 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 Shaft Non-Mechanical Work Non-mechanical work generally involves microscopic motion Electrical work Polarization work Magnetic Work Next Time Read: 2.6-2.7 Homework: Chapter 2, P: 37, 46, 57, 63
