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Thermodynamics
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CHAPTER 3.2 ENERGY TRANSFER BY HEAT AND
WORK
(2.4, 2.5, 4.1)
Lecture
Date:
3/22/2015 Thermodynamics I 1
2.4 Energy Transfer by Work
3/22/2015 Thermodynamics I 2
Work, like heat, is an energy interaction between a system and its surroundings.
As mentioned earlier, energy can cross the boundary of a closed system in the form of heat or work.
Therefore, if the energy crossing the boundary of a closed system is not heat, it must be work.
Heat is easy to recognize: Its driving force is a temperature difference between the system and its surroundings.
Then we can simply say that an energy interaction that is not caused by a temperature difference between a system and its surroundings
is work.
Work is the energy transfer associated with a force acting through a distance.
2.4 Energy Transfer by Work
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Work Done Per Unit Mass
Work is also a form of energy transferred like heat and, therefore, has energy units such as kJ.
The work done during a process between states 1 and 2 is denoted by W12, or simply W.
The work done per unit mass of a system is denoted by w and is expressed as
The work done per unit time is called power and is denoted W.
The unit of power is kJ/s, or kW.
2.4 Energy Transfer by Work
3/22/2015 Thermodynamics I 4
Sign Convention for Work
(W > 0): Work is done by the system
(W < 0): Work is done on the system
2.4 Energy Transfer by Work
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Similarity Between Heat and Work
Heat and work are energy transfer mechanisms between a system and
its surroundings, and there are many similarities between them:
2.4 Energy Transfer by Work
3/22/2015 Thermodynamics I 6
Differential for Point Functions and State Functions
Point functions (i.e., they depend on the state only, and not on how a
system reaches that state), and they have exact differentials designated
by the symbol d.
A small change in volume, for example, is represented by dV,
Path functions have inexact differentials designated by the symbol .
Therefore, a differential amount of heat or work is represented by Q
or W, respectively, instead of dQ or dW.
2.4 Energy Transfer by Work
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Electrical Work
In an electric field, electrons in a wire move under the effect of
electromotive forces, doing work.
When N coulombs of electrical charge move
through a potential difference V, the electrical
work done is
which can also be expressed in the rate form as
where,
V : Voltage, Volt
I : Current, Ampere
2.4 Energy Transfer by Work
3/22/2015 Thermodynamics I 8
Electrical Work
In general, both V and I vary with time, and the electrical work done
during a time interval t is expressed as
2.4 Energy Transfer by Work
3/22/2015 Thermodynamics I 9
Mechanical Work
There are several different ways of doing work, each in some way
related to a force acting through a distance.
The work done by a constant force F on a body displaced a distance s
in the direction of the force is given by:
If the force F is not constant, the work done is obtained by adding (i.e.,
integrating) the differential amounts of work,
The work done on a system by an external force acting in the direction
of motion is negative, and work done by a system against an external
force acting in the opposite direction to motion is positive.
2.4 Energy Transfer by Work
3/22/2015 Thermodynamics I 10
Mechanical Work
1. Gravitational Work
2. Acceleration Work
3. Shaft Work
4. Spring Work
5. Moving Boundary Work
@ Constant Volume, @ Constant Pressure, @ Constant Temperature
Polytropic Process
2.4 Energy Transfer by Work
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1. Gravitational Work
Work required to move an object against force of gravity.
W = F ds
where F = mg and s = z
Therefore,
Wg = mg.dz z: elevation
Wg = mg (z2 z1) = PE2 PE1 ( z2 > z1)
Example 2-8
2.4 Energy Transfer by Work
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2. Acceleration Work
When a body is raised in a gravitational field, its potential energy
increases. Likewise, when a body is accelerated, its kinetic energy
increases.
Wa = m (v22 v1
2)/2 = KE2 KE1 (v2 > v1)
Example 2-9
2.4 Energy Transfer by Work
3/22/2015 Thermodynamics I 13
3. Shaft Work
Energy transmission with a rotating shaft is very common in
engineering practice.
The power transmitted through the shaft is the shaft work done per unit
time, which can be expressed as
n = number of revoultions per unit time
T = torque
Example 2-7
2.4 Energy Transfer by Work
3/22/2015 Thermodynamics I 14
4. Spring Work
Work involved in elongating or compressing a spring from rest
position.
W = F ds
Since F = k x for a linear spring
Take s = x or ds = dx
Therefore,
4.1 Moving Boundary Work
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One form of mechanical work frequently encountered in practice is
associated with the expansion or compression of a gas in a piston
cylinder device.
During this process, part of the boundary (the inner face of the piston)
moves back and forth.
Therefore, the expansion and compression work is often called moving
boundary work, or simply boundary work (Fig. 41).
Gas
s s ds s1 s2
4.1 Moving Boundary Work
3/22/2015 Thermodynamics I 16
The total boundary work done during the entire process as the piston
moves is obtained by adding all the differential works from the initial
state to the final state:
This integral can be evaluated only
if we know the functional
relationship between P and V
during the process. That is, P = f
(V) should be available.
4.1 Moving Boundary Work
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The area under the process curve on a P-V
diagram represents the boundary work.
2
1P dV WbArea
P
1 2
Process
4.1 Moving Boundary Work
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A gas can follow several different paths as
it expands from state 1 to state 2.
In general, each path will have a different
area underneath it, and since this area
represents the magnitude of the work, the
work done will be different for each
process.
This is expected, since work is a path
function (i.e., it depends on the path
followed as well as the end states).
4.1 Moving Boundary Work
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Constant Volume Process:
@ Constant volume:
Wb = P dV
Therefore,
Wb = 0 at constant volume
if V = constant, then dV = 0
4.1 Moving Boundary Work
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Constant Pressure Process:
@ Constant Pressure (P = Po = constant )
Wb = P dV
Then,
Wb = Po (V2 V1)
= Po V
4.1 Moving Boundary Work
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Expansion of gas against spring:
4.1 Moving Boundary Work
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Constant Temperature:
Case 1: For an in Ideal gas law in a closed system
4.1 Moving Boundary Work
3/22/2015 Thermodynamics I 23
Constant Temperature:
Case 1: For systems involving liquids or phase changes
PROCEDURE:
1. Define phases of initial and final
states
2. Obtain properties of initial and
final phases as well as saturation
conditions
3. Draw the process path on a P-v
diagram (see the figure)
4. Calculate the area under the curve
(rectangles, trapezoids, etc.) v
T
const.
P
4.1 Moving Boundary Work
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Adiabatic Process:
4.1 Moving Boundary Work
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Adiabatic Process:
4.1 Moving Boundary Work
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Polytropic process:
4.1 Moving Boundary Work
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Polytropic process:
During actual expansion and compression processes of gases,
pressure and volume are often related by PVn = C, where n and C are
constants.
4.1 Moving Boundary Work
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Polytropic process:
How to find the exponent n ----
Method 1: by plotting data
By plotting ln(P) vs ln(V) intercept = ln(C); slope = n
Method 2: From two data points
Example
3/22/2015 Thermodynamics I 29
SOLUTION:
Assuming Ideal Gas Behavior
Example
3/22/2015 Thermodynamics I 30
Since we have a polytropic process: