11/19/2013phy 113 c fall 2013 -- lecture 231 phy 113 c general physics i 11 am – 12:15 pm mwf olin...
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PHY 113 C Fall 2013 -- Lecture 23 111/19/2013
PHY 113 C General Physics I11 AM – 12:15 PM MWF Olin 101
Plan for Lecture 23:Chapter 22: Heat engines
1. Thermodynamic cycles; work and heat efficiency
2. Carnot cycle3. Otto cycle; diesel cycle4. Brief comments on entropy
PHY 113 C Fall 2013 -- Lecture 23 211/19/2013
PHY 113 C Fall 2013 -- Lecture 23 311/19/2013
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 code
PHY 113 C Fall 2013 -- Lecture 23 411/19/2013
Important equations for macroscopic and microscopic descriptions of thermodynamic properties of matter
1 :/ with moleculesFor
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) massmolar of moles or mass of molecules (assume
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: WorkmicThermodyna
:micsThermodyna of LawFirst
int
2
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PdVW
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rms
rmsrms
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V
f
i
PHY 113 C Fall 2013 -- Lecture 23 511/19/2013
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?
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nRTMvnvmNPV
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mN
rms
rmsrms
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) massmolar of moles
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:molecules gas of analysis kinetic theFrom
PHY 113 C Fall 2013 -- Lecture 23 611/19/2013
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.
DEint = Q + 0 = 213J + 0 = 213 J
ifV TTnCQ
PHY 113 C Fall 2013 -- Lecture 23 711/19/2013
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. (a) What is the final pressure of the gas?(b) What are the initial and final temperatures?(c) Find Q for the gas during this process.(d) Find ΔEint for the gas during this process.(e) Find W for the gas during this process.
PHY 113 C Fall 2013 -- Lecture 23 811/19/2013
Digression: Adiabatic process (Q=0)
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γ
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int
PHY 113 C Fall 2013 -- Lecture 23 911/19/2013
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.
(a) What is the final pressure of the gas?
b) What are the initial and final temperatures?PV=nRT
c) Find Q for the gas during this process. Q=0d) Find ΔEint for the gas during this process. ΔEint=We) Find W for the gas during this process.
For diatomic ideal gas: = 1.4g
4.1
γγ
12.2/29.6atm06.5/
fiif
ffii
VVPP
VPVP
PHY 113 C Fall 2013 -- Lecture 23 1011/19/2013
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)?
PHY 113 C Fall 2013 -- Lecture 23 1111/19/2013
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?
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PHY 113 C Fall 2013 -- Lecture 23 1211/19/2013
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 1.4
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:process adiabatican For
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11
int
PHY 113 C Fall 2013 -- Lecture 23 1311/19/2013
Thermodynamic cycles for designing ideal engines and heat pumps
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3 x
105 )
Pa
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Pf
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B C
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eng
outin
eng
Q
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:Efficiency
:system input toHeat
:engine ofWork
Engine process:
http://auto.howstuffworks.com/engine1.htm
PHY 113 C Fall 2013 -- Lecture 23 1411/19/2013
P (
1.01
3 x
105 )
Pa
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Pi
Pf
A
B C
D
Examples process by an ideal gas:
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Q
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)( iff PPV 1-γ
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)( iff PPV 1-γ
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)( ifi VV-P
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in
eng
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Q
W
:Efficiency
PHY 113 C Fall 2013 -- Lecture 23 1511/19/2013
Example from homework
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eng
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:Also
PHY 113 C Fall 2013 -- Lecture 23 1611/19/2013
Most efficient thermodynamic cycle -- Carnot
Sadi Carnot 1796-1832
PHY 113 C Fall 2013 -- Lecture 23 1711/19/2013
Carnot cycle:
AB Isothermal at Th
BC AdiabaticCD Isothermal at Tc
DA Adiabatic
h
c
in
out
in
outin
T
Tε
Q
Q
Q
1
1
cycleCarnot of Efficiency
PHY 113 C Fall 2013 -- Lecture 23 1811/19/2013
iclicker exercise:We discussed the efficiency of an engine as
Is this resultA. Special to the Carnot cycleB. General to all ideal thermodynamic cycles
iclicker exercise:We discussed the efficiency of an engine running with hot and cold reservoirs as
Is this resultA. Special to the Carnot cycleB. General to all ideal thermodynamic cycles
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PHY 113 C Fall 2013 -- Lecture 23 1911/19/2013
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PHY 113 C Fall 2013 -- Lecture 23 2011/19/2013
iclicker exercise:Why should we care about the Carnot cycle?
A. We shouldn’tB. It approximately models some
heating and cooling technologiesC. It provides insight into another
thermodynamic variable -- entropy
PHY 113 C Fall 2013 -- Lecture 23 2111/19/2013
PHY 113 C Fall 2013 -- Lecture 23 2211/19/2013
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?
36215.273
2815.27311
:res temperatucold andhot between
operating processefficient most theis cycleCarnot The
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c
T
T
PHY 113 C Fall 2013 -- Lecture 23 2311/19/2013
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.
(a) Find the energy expelled to the cold reservoir in each cycle.
(b) (b) Find the net work done by the gas in each cycle.
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c
h
c
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126015.273
5015.27311
PHY 113 C Fall 2013 -- Lecture 23 2411/19/2013
The Otto cycle
1
1
21
:efficiency lTheoretica
V
V
V1/V2 is the “compression ratio” -- typically V1/V2 = 8 e=0.56
PHY 113 C Fall 2013 -- Lecture 23 2511/19/2013
PHY 113 C Fall 2013 -- Lecture 23 2611/19/2013
The Diesel cycle
BC
AD
TT
TT
1
1
:efficiency lTheoretica
In principle, higher efficiency than comparable Otto cycle.
PHY 113 C Fall 2013 -- Lecture 23 2711/19/2013
Engine vs heating/cooling designs
(Carnot)
: mode heating pump;Heat
ch
hh
TT
T
W
Q
(Carnot)
: mode cooling pump;Heat
ch
cc
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T
W
Q
PHY 113 C Fall 2013 -- Lecture 23 2811/19/2013
Brief comments about entropy – macroscopic picture
Carnot cycle
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)/ln(
)/ln(
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11
11
PHY 113 C Fall 2013 -- Lecture 23 2911/19/2013
Brief comments about entropy – continued
) (like variable"state"
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