Transcript Mechanical 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 = 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