PHY 113 C Fall 2013 Lecture 23 1 PHY 113 C General Physics I 11 AM 1215 P M MWF Olin 101 Plan for Lecture 23 Chapter 22 Heat engines Thermodynamic cycles work and heat efficiency ID: 201999
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11/19/2013
PHY 113 C Fall 2013 -- Lecture 23
1
PHY 113 C General Physics I
11 AM – 12:15
P
M MWF Olin 101
Plan for Lecture 23:
Chapter 22: Heat engines
Thermodynamic cycles; work and heat efficiency
Carnot cycle
Otto cycle; diesel
cycle
Brief comments on entropySlide2
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PHY 113 C Fall 2013 -- Lecture 23
2Slide3
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PHY 113 C Fall 2013 -- Lecture 23
3
Comment about Exam 3:
Part I – take home portion (1 problem): available Thursday 11/21/2013 after class; must be turned in before Part II – in-class portion (3 problems): Tuesday 11/25/2013
Some special arrangements for early exams have been (or will be) arranged by
prior agreement
Of course, all sections of the exam are to be taken under the guidelines of the honor codeSlide4
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PHY 113 C Fall 2013 -- Lecture 23
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Important equations for macroscopic and microscopic descriptions of thermodynamic properties of matterSlide5
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Webassign
– Assignment 20
The
rms
speed of an oxygen molecule (O2) in a container of oxygen gas is 563 m/s. What is the temperature of the gas?Slide6
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PHY 113 C Fall 2013 -- Lecture 23
6
Webassign
– Assignment 20
In a constant-volume process, 213 J of energy is transferred by heat to 0.99
mol
of an ideal monatomic gas initially at 299 K. (a) Find the work done on the gas.
(b) Find the increase in internal energy of the gas.
(
c) Find its final temperature.
For constant volume process, W=0.
D
E
int
= Q + 0 = 213J + 0 = 213 JSlide7
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PHY 113 C Fall 2013 -- Lecture 23
7
Webassign
– Assignment 20
A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.06
atm
and a volume of 12.2 L to a final volume of 29.6 L.
What
is the final pressure of the gas
?
What are the initial and final temperatures
?
Find
Q
for the gas during this process
.
Find
Δ
E
int
for the gas during this process
.
Find
W
for the gas during this process.Slide8
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PHY 113 C Fall 2013 -- Lecture 23
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Digression:
Adiabatic process (Q=0)Slide9
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Webassign
– Assignment 20
A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.06
atm
and a volume of 12.2 L to a final volume of 29.6 L.
What
is the final pressure of the gas
?
What
are the initial and final temperatures
?
PV=
nRT
Find
Q
for the gas during this process
.
Q=0
Find
Δ
E
int
for the gas during this process
.
ΔE
int
=W
Find
W for the gas during this process.
For diatomic ideal gas:
g = 1.4Slide10
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PHY 113 C Fall 2013 -- Lecture 23
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Webassign
– Assignment 20
(a) How much work is required to compress 4.95
mol
of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an isothermal process?
(b) How much work is required to produce the same compression in an adiabatic process?
(c) What is the final pressure in part (a)?
(d) What is the final pressure in part (b)?Slide11
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Webassign
– Assignment 20
(a) How much work is required to compress 4.95
mol
of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an isothermal process?Slide12
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Webassign
– Assignment 20
(b)
How much work is required to compress 4.95
mol of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an adiabatic process
? Note
: assume
g=1.4Slide13
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Thermodynamic cycles for designing ideal engines and heat pumps
P (1.013 x 10
5
) Pa
V
i
V
f
P
i
P
f
A
B
C
D
Engine process:
http://auto.howstuffworks.com/engine1.htmSlide14
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P (1.013 x 10
5
) Pa
V
i
V
f
P
i
P
f
A
B
C
D
Examples process by an ideal gas:
A
®
B
B
®
C
C
®
D
D
®
A
Q
W
0
-P
f
(
V
f
-V
i
)
0
P
i
(
V
f
-V
i
)
D
E
intSlide15
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Example from homeworkSlide16
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Most efficient thermodynamic cycle -- Carnot
Sadi
Carnot 1796-1832Slide17
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Carnot cycle:
A
B Isothermal at
T
h
BC Adiabatic
CD Isothermal at
T
c
DA AdiabaticSlide18
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iclicker
exercise
:
We discussed the efficiency of an engine as
Is this result
Special to the Carnot cycle
General to all ideal thermodynamic cycles
iclicker
exercise
:
We discussed the efficiency of an engine running with hot and cold reservoirs as
Is this result
Special to the Carnot cycle
General to all ideal thermodynamic cyclesSlide19
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For Carnot cycle:Slide20
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iclicker
exercise:
Why should we care about the Carnot cycle?
We shouldn’t
It approximately models some heating and cooling technologies
It provides insight into another thermodynamic variable -- entropySlide21
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21Slide22
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Webassign
Assignment 21
A heat engine operates between a reservoir at 28°C and one at 362°C. What is the maximum efficiency possible for this engine?Slide23
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Webassign
Assignment 21
An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 260
°
C, and the isothermal compression takes place at 50.0°C. The gas takes in 1.28 x103
J of energy from the hot reservoir during the isothermal expansion.
Find
the energy expelled to the cold reservoir in each cycle.
(
b) Find the net work done by the gas in each cycle.Slide24
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The Otto cycle
V
1
/V
2
is the “compression ratio” -- typically
V
1
/V
2
= 8
e
=0.56Slide25
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25Slide26
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The Diesel cycle
In principle, higher efficiency than comparable Otto cycle.Slide27
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Engine
vs
heating/cooling designsSlide28
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Brief comments about entropy – macroscopic picture
Carnot cycle Slide29
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Brief comments about entropy – continued