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 =  gh  P top = (13600)(9.8)(0.730) =  P bottom = (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   P =  gh = 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 = ½mv 2   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  e mech = (P/r)+(v 2 /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:   E’ mech = m’[(  P/r)+(  V 2 )/2)+g(  z)]   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,  W  Thus the total work is:  The total work is the sum of all the small differential works (  W) 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(x 2 2 -x 2 1 )  Stretched Film (2D):   W = ∫  s 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)(2  rn) = 2  nT  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:  Homework: Chapter 2, P: 37, 46, 57, 63