Upload
lynette-barrett
View
222
Download
0
Tags:
Embed Size (px)
Citation preview
Accounting for Energy - Part 2
Chapter 22 b
Objectives Know that energy is conserved Understand state energies
Kinetic, Potential, Internal Understand flow work Understand sequential energy
conversion Be able to do calculations involving
accounting for energy
Recall...Accumulation = Net Input + Net Gen
State Energies• Kinetic• Potential• Internal
(Independent of Path)
Path Energies• Work• Heat(Depend on Path)
0(Energy is conserved)
Previous focusCurrent focus
State Energies State energies do not depend on
path. Three kinds:
Kinetic Potential Internal
Often specified by other state quantities (e.g., velocity, height, temperature, pressure)
Kinetic Energy Energy associated with a moving
mass. Often mechanical or shaft work is
used to produce kinetic energy. Example:
Shaft work from a car engine produces the car’s kinetic energy.
Kinetic Energy
A rigid mass accelerates from an initial velocity v1 to a final velocity v2 because of applied force, F.
Thus, an input of mechanical work causes the object to change its kinetic energy, Ek
Initial stateF
v1
F
v2Dx
Final state
Kinetic EnergyFrom the UAE
Energyfinal - Energyinitial = Net Input
Thus, for a constant force F:DEk = Net Mech. Work Input = FDx
After applying Newton’s Laws we getDEk = ½ mv2
2 - ½ mv12
(see p. 584 Foundations of Engineering for derivation)
Potential Energy Potential energy is associated with
the interactions with other bodies. It is always between two or more items
Examples: Gravitational potential Spring potential Others: electrical (capacitors),
magnetic (inductors), hydraulic (pumped storage)
Gravitational Potential Consider a rigid mass
lifted vertically by a force F a distance Dx.
Thus, an input of mechanical work changes the object’s potential energy, Ep
Fup
Fdn = mgDx
Gravitational Potential
From the UAE:Energyfinal - Energyinitial = Net Input
Thus, for a constant force F:DEp = Net Mech. Work Input = FDx
The force acting on the mass is F = mg
so DEp = mgDx
Pairs Exercise #1
A 4000-kg elevator starts from rest, accelerates uniformly to a constant speed of 1.8 m/s, and decelerates uniformly to stop 20 m above its initial position. Neglecting friction and other losses, what work was done on the elevator?
20 mM = 4000 kg
+
+
+ Data
Solution to Pairs Exercise #1
Spring Potential Energy Consider a force F compressing a
spring a distance Dx. (See p. 587 Foundations of Engineering)
Thus, an input of mechanical work causes the spring’s potential energy to change.
From the UAE:Energyfinal - Energyinitial = Net Input
DEp = Net Mech. Work Input
Spring Potential Energy
This time the force is not constant along x. By Hook’s Law, the relationship is
F=kxwhere k is the spring constant and x=0 is the uncompressed (relaxed) state.
)( 21
222
1
2
1
2
1
xxk
kxdx
FdxE
x
x
x
x
p
Internal Energy The energy stored inside the
medium. The energy associated with
translational, rotational, vibrational, and electronic potential energy of atoms and molecules.
Internal Energy
Translation
Rotation
Vibration
MolecularInteractions
Review: States of Matter
Solid Liquid
Gas Plasma
Review: Phase Diagram
Plasma
Gas
Vapor
Liquid
Solid
Ttriple Tcritical
Ptriple
Pcritical
Pressure
Temperature
Critical Point
TriplePoint
No Phase Change (Sensible Energy)
When path energy (heat, work) is added to a material, IF THERE IS NO PHASE CHANGE, temperature increases.
This added energy changes the internal energy of the medium,
Ufinal - Uinitial = DU = Net Path Energy Input
Heat Capacity for Constant- Volume Processes (Cv)
Heat is added to a substance of mass m in a fixed volume enclosure, which causes a change in internal energy, U. Thus,
Q = U2 - U1 = DU = m Cv DTThe v subscript implies constant volume
Heat, Qaddedm m
DTinsulation
Heat Capacity for Constant- Pressure Processes (Cp)
Heat is added to a substance of mass m held at a fixed pressure, which causes a change in internal energy, U, AND some PV work.
Heat, Qadded
DT
m m
Dx
Cp Defined
Thus,Q = DU + PDV = DH = m Cp DT
The p subscript implies constant pressure
Note: H, enthalpy. is defined as U + PV, so dH = d(U+PV) = dU + VdP + PdV
At constant pressure, dP = 0, so dH= dU + PdV
For large changes at constant pressure
DH = DU + PDV
Phase Changes(Latent Energy) When path energy (heat, work) is
added to a material, IF THERE IS A PHASE CHANGE AT CONSTANT PRESSURE, temperature stays constant.
Examples… boiling water melting ice cubes
Total Energy Conservation For a closed system (no mass in or
out):DEk + DEp + DU = Win - Wout + Qin - Qout
For an open system, with M defined as energy entering or leaving the system with the mass:
DEk + DEp + DU = Win - Wout + Qin - Qout + Min - Mout
Flow Energies In open systems, we must consider
the flow of energy across the system boundary due to mass flow.
The mass flow rate is indicated by Potential: Kinetic: Etc.
ininoutoutp gzmgzmE 2
212
21
ininoutoutk vmvmE
m
Sequential Energy Conversion
Step 1 Step 2 Step 3E1
E2 E3E4
h1 h2 h3
hoverall =h1h2h3
Pair Exercise #2
An incandescent lamp is powered by electricity from a coal-fired electric plant. To produce 10 W of visible light, what is the required rate of heat release (W) from coal combustion? (Hint: See Figure 22.30)
Individual Exercise #1 Solve the problem outlined on the
next slides Document your steps Solution will be turned in
separately
Bungee Jumping Exercise
George is going to bungee jump from a bridge that is 195 meters above a river on a cord with a taut length of 50.0 meters
taut length = length of unstretched cord
prior to reaching the taut length, the cord exerts no force and George is in freefall
More...
Bungee Jumping Exercise Once the taut length is reached, use the
following equation to determine the force on George due to the bungee cord:
F=(15 kg/s2)(X-Xtaut) You may neglect air drag in all tasks. You may assume this is a one-dimensional
motion problem, i.e., you may assume that George falls straight down and on the rebound follows the same path upward.
More...
Bungee Jumping Exercise1. George has a mass of 75 kg.
Determine his velocity at the instant the cord becomes taut.
2. Determine the maximum distance George will travel from the bridge and the minimum distance from the bridge once he bounces back.
3. Determine the maximum mass of person that can jump from bridge and NOT impact the river.
15 minutes
Be prepared to turn in your well-documented solution 15 minutes from now.
Team Exercise #1 (10 minutes)
As a team.. compare answers resolve differences prepare a team solution
Submit team solution original solutions from each team
member