Download heat engine

Chemistry 2402 - Thermodynamics
Lecture 7 : Entropy
Lecture 8 : Converting Heat to Work
Lecture 9: Free Energies
Aim
The aim of this course is to develop the general principles that
govern all equilibrium states.
We shall base everything on two results from the statistics of
energy distribution:
1. the equilibrium state of an isolated system is that which
maximises the entropy. (2nd Law of thermodynamics)
2. dS = q/T where q is the (reversible) heat flow into the
system
REFLECTIONS
ON THE
MOTIVE POWER
OF FIRE
AND ON MACHINES FITTED TO
DEVELOP THIS POWER
BY
S. CARNOT
1824
This image is in the public domain because its copyright has
expired.
http://commons.wikimedia.org/wiki/Image:Sadi_Carnot.jpeg
Thermodynamics and Engines
A system that converts
heat flow into work and
does so in a cyclic way
(i.e. so that it can, in
principle, go on doing it
indefinitely) is called an
engine (or, sometimes, a
heat engine).
If we run such an engine
in reverse, i.e. do work to
produce a heat flow, we
have a refrigerator.
Desktop Stirling Engine
Source: Richard Wheeler
http://commons.wikimedia.org/wiki
/Image:Stirling_Engine.jpg
Early refrigerator
Source: Mike Manning
http://en.wikipedia.org/wiki
/Image:Monitor_refer.jpg
The Newcomen Engine
The first application of
steam engines was to
pump water from mines.
James Watt realised that
reheating the cooled
cylinder wasted heat. He
introduced a separate
condenser - the increase in
efficiency contributed to
the Industrial Revolution.
This image is in the public domain because its copyright has expired.
http://en.wikipedia.org/wiki/Image:Newcomen6325.png
A Simple Engine
Th
A
Th
D
B
Tc
Tc
C
A - an isothermal (i.e.
constant temperature)
expansion at Th against a
fixed pressure PA
B - cooling from Th to Tc at
a fixed volume
C - an isothermal
compression at Tc at the new
fixed pressure PC
D - heating from Tc to Th at
a fixed volume
Keeping the energy account
We can reduce the engine to a path between equilibrium states.
A
work out
Th
T
D
B
Tc
C
V
Heat is absorbed in steps D and A, heat is released in steps B and C.
Converting Heat to Work
All engines can be described as follows.
hot bath T h
qin
wout
engine
qout
cold bath T c
From conservation of energy, wout = qin –qout
Why does there have to be any qout at all?
Why must we waste heat?
Consider the simpler process of transferring heat from the hot bath to the cold
i.e. get rid of the engine.
hot bath Th
qin = qout
cold bath Tc
S = -qin/Th + qin/Tc > 0 because Th > Tc
For this process to be spontaneous (i.e. happen) heat MUST flow into the cold bath.
What is the minimum amount of lost heat?
What is the smallest amount of heat we need to discard to the cold bath so that
the overall cycle remains allowed, i.e. S = 0 (as opposed to spontaneous for
which S > 0)?
Answer: If S = -qin/Th+ qout/Tc = 0 then qout = qin Tc/Th
and the maximum work output is
wout = qin - qout = qin (1-Tc/Th)
Or an efficiency of wout/qin = 1-Tc/Th
100% efficiency can only be obtained when the cold bath is at absolute zero.
Kelvin’s Temperature Scale
In fact, the relation
qin/qout = Th /Tc
is only satisfied by an
absolute temperature
scale. This is how
Kelvin settled on this
scale in the first place.
"heavier-than-air flying machines
are impossible" Kelvin 1895
"There is nothing new to be
discovered in physics now. All that
remains is more and more precise
measurement." Kelvin 1900
This image is in the public domain because its copyright has expired.
What is the smallest
amount of electrical
work required to remove
1 J of energy from a
freezer at -5 °C, when
the surrounding
temperature is 25 °C?
Flash Quiz!
hot bath Th (surrounds)
qout
refridgeration
unit
qin
cold bath Tc (freezer)
Win
a) 0 J
b) less than 1 J
c) exactly 1 J
d) more than 1 J
Hints
What is the smallest amount of electrical work
required to remove 1 J of energy from a
freezer at -5 °C, when the surrounding
temperature is 25 °C?
“smallest energy” → most efficient,
so
S = +qout/Th - qin/Tc = 0
hot bath Th (surrounds)
qout
refridgeration
unit
qin
cold bath Tc (freezer)
Win
conservation of energy (first law) also means
win + qin = qout
Answer
What is the smallest amount of electrical work
required to remove 1 J of energy from a
freezer at -5 °C, when the surrounding
temperature is 25 °C?
“smallest energy” → most efficient,
so
S = +qout/Th - qin/Tc = 0
qout = qin × Th / Tc
hot bath Th (surrounds)
qout
refridgeration
unit
qin
cold bath Tc (freezer)
Win
conservation of energy (first law) also means
win + qin = qout
so
win = qin ( Th/Tc - 1)
= 1J×(298K/268K - 1)
= 0.11 J
this is much higher on hotter days or if you set
your freezer temperature really cold
How do we make an engine that runs at
maximum efficiency?
Consider the work obtained from an expansion at constant temperature.
pressure
Let’s hold a piston+cylinder at volume V1 with a pressure P1 and then drop the
pressure to P2 let it expand freely to V2
P1
P2
V1
V2
volume
The work obtained is the shaded area.
Slower is better
pressure
Let’s now do this expansion in a number of pressure steps.
P1
P2
V1
V2
volume
The work on the surrounding (i.e. the shaded area) has increased.
Reversible and Irreversible Processes
pressure
In the limit of infinitely many small pressure steps we find the state of the gas
in the cylinder always remains very close to the equilibrium volume for the
pressure and the maximum work is obtained.
P1
P2
V1
V2
volume
This infinitely gradual process is called a quasi-static or reversible process.
All real processes – i.e. ones that occur in a finite time – are irreversible.
Heat Engine Examples
Sources
Left: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.html
Top right: http://www.ent.ohiou.edu/~thermo/me321/quiz.info/
StirlCogen/StirlCogen.html
Bottom right: http://www.grc.nasa.gov/WWW/K-12/airplane/otto.html
Sample exam questions from
previous years
• Provide a brief explanation of each of the
following terms:
– heat engine
– reversible process
Summary
You should now
• Be able to explain the role of heat and work in an engine
• Understand the significance of the Kelvin temperature scale
• Be able to represent an engine by a thermodynamic cycle
• Know the connection between a path on a P-V plot, and the
work generated by an engine carrying out that path
• Be able to calculate the maximum efficiency for an ideal
engine or refrigerator
• Explain the thermodynamic meaning of a reversible process
Next Lecture
• Free energies