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 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

P = gh = 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: E’mech = m’[(P/r)+(V2)/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(x22-x2

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)(2rn) = 2nT 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