Second Law of Thermodynamics

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Second Law of Thermodynamics
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• The Second Law of ThermodynamicsIntroduction
• Heat Engines
• Reversible and Irreversible Processes the
  Carnot Engine
• Refrigerators, Air Conditioners, and Heat Pumps
• Entropy
• Entropy and the Second Law of Thermodynamics

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• Order to Disorder
• Unavailability of Energy Heat Death
• Statistical Interpretation of Entropy and the
  Second Law
• Thermodynamic Temperature Third Law of
  Thermodynamics
• Thermal Pollution, Global Warming, and Energy
  Resources

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The Second Law of ThermodynamicsIntroduction
The first law of thermodynamics tells us that
energy is conserved. However, the absence of the
process illustrated above indicates that
conservation of energy is not the whole story. If
it were, movies run backwards would look
perfectly normal to us!
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The Second Law of ThermodynamicsIntroduction
The second law of thermodynamics is a statement
about which processes occur and which do not.
There are many ways to state the second law here
is one Heat can flow spontaneously from a hot
object to a cold object it will not flow
spontaneously from a cold object to a hot object.
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Heat Engines
It is easy to produce thermal energy using work,
but how does one produce work using thermal
energy?
This is a heat engine mechanical energy can be
obtained from thermal energy only when heat can
flow from a higher temperature to a lower
temperature.
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Heat Engines
We will discuss only engines that run in a
repeating cycle the change in internal energy
over a cycle is zero, as the system returns to
its initial state. The high-temperature reservoir
transfers an amount of heat QH to the engine,
where part of it is transformed into work W and
the rest, QL, is exhausted to the lower
temperature reservoir. Note that all three of
these quantities are positive.
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Heat Engines
A steam engine is one type of heat engine.
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Heat Engines
The internal combustion engine is a type of heat
engine as well.
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Heat Engines
Why does a heat engine need a temperature
difference? Otherwise the work done on the system
in one part of the cycle would be equal to the
work done by the system in another part, and the
net work would be zero.
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Heat Engines
The efficiency of the heat engine is the ratio of
the work done to the heat input
Using conservation of energy to eliminate W, we
find
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Heat Engines

• Car efficiency.
• An automobile engine has an efficiency of 20 and
  produces an average of 23,000 J of mechanical
  work per second during operation.
• How much heat input is required, and
• (b) How much heat is discharged as waste heat
  from this engine, per second?

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Heat Engines
No heat engine can have an efficiency of 100.
This is another way of writing the second law of
thermodynamics No device is possible whose sole
effect is to transform a given amount of heat
completely into work.
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Reversible and Irreversible Processes the Carnot
Engine

• The Carnot engine was created to examine the
  efficiency of a heat engine. It is idealized, as
  it has no friction. Each leg of its cycle is
  reversible.
• The Carnot cycle consists of
• Isothermal expansion
• Adiabatic expansion
• Isothermal compression
• Adiabatic compression

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Reversible and Irreversible Processes the Carnot
Engine
For an ideal reversible engine, the efficiency
can be written in terms of the temperature
From this we see that 100 efficiency can be
achieved only if the cold reservoir is at
absolute zero, which is impossible. Real engines
have some frictional losses the best achieve
6080 of the Carnot value of efficiency.
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Reversible and Irreversible Processes the Carnot
Engine
A phony claim? An engine manufacturer makes the
following claims An engines heat input per
second is 9.0 kJ at 435 K. The heat output per
second is 4.0 kJ at 285 K. Do you believe these
claims?
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Reversible and Irreversible Processes the Carnot
Engine
Automobiles run on the Otto cycle, shown here,
which is two adiabatic paths alternating with two
constant-volume paths. The gas enters the engine
at point a and is ignited at point b. Curve cd is
the power stroke, and da is the exhaust.
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Reversible and Irreversible Processes the Carnot
Engine

• The Otto cycle.
• Show that for an ideal gas as working substance,
  the efficiency of an Otto cycle engine is
• e 1 (Va/Vb)1-?
• where ? is the ratio of specific heats (?
  CP/CV) and Va/Vb is the compression ratio.
• (b) Calculate the efficiency for a compression
  ratio Va/Vb 8.0 assuming a diatomic gas like O2
  and N2.

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Solution
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Solution
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Refrigerators, Air Conditioners, and Heat Pumps
These appliances are essentially heat engines
operating in reverse.
By doing work, heat is extracted from the cold
reservoir and exhausted to the hot reservoir.
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Refrigerators, Air Conditioners, and Heat Pumps
This figure shows more details of a typical
refrigerator.
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Refrigerators, Air Conditioners, and Heat Pumps
Refrigerator performance is measured by the
coefficient of performance (COP)
Substituting
For an ideal refrigerator,
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Refrigerators, Air Conditioners, and Heat Pumps
Making ice. A freezer has a COP of 3.8 and uses
200 W of power. How long would it take this
otherwise empty freezer to freeze an ice-cube
tray that contains 600 g of water at 0C?
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Refrigerators, Air Conditioners, and Heat Pumps
A heat pump can heat a house in the winter
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Refrigerators, Air Conditioners, and Heat Pumps
Heat pump. A heat pump has a coefficient of
performance of 3.0 and is rated to do work at
1500 W. (a) How much heat can it add to a room
per second? (b) If the heat pump were turned
around to act as an air conditioner in the
summer, what would you expect its coefficient of
performance to be, assuming all else stays the
same?
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Entropy
Definition of the change in entropy S when an
amount of heat Q is added
if the process is reversible and the temperature
is constant. Otherwise,
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Entropy
Any reversible cycle can be written as a
succession of Carnot cycles therefore, what is
true for a Carnot cycle is true of all reversible
cycles.
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Entropy
Since for any Carnot cycle QH/TH QL/TL 0, if
we approximate any reversible cycle as an
infinite sum of Carnot cycles, we see that the
integral of dQ/T around a closed path is zero.
This means that entropy is a state variablethe
change in its value depends only on the initial
and final states.
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Entropy and the Second Law of Thermodynamics
Entropy change when mixing water. A sample of
50.0 kg of water at 20.00C is mixed with 50.0 kg
of water at 24.00C. Estimate the change in
entropy.
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Entropy and the Second Law of Thermodynamics
The total entropy always increases when heat
flows from a warmer object to a colder one in an
isolated two-body system. The heat transferred is
the same, and the cooler object is at a lower
average temperature than the warmer one, so the
entropy gained by the cooler one is always more
than the entropy lost by the warmer one.
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Entropy and the Second Law of Thermodynamics
Entropy changes in a free expansion. Consider the
isothermal expansion of n moles of an ideal gas
from volume V1 to volume V2, where V2 gt V1.
Calculate the change in entropy (a) of the gas
and (b) of the surrounding environment. (c)
Evaluate ?S for 1.00 mole, with V2 2.00 V1.
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Entropy and the Second Law of Thermodynamics
Heat transfer. A red-hot 2.00-kg piece of iron at
temperature T1 880 K is thrown into a huge lake
whose temperature is T2 280 K. Assume the lake
is so large that its temperature rise is
insignificant. Determine the change in entropy
(a) of the iron and (b) of the surrounding
environment (the lake).
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Entropy and the Second Law of Thermodynamics
The fact that after every interaction the entropy
of the system plus the environment increases is
another way of putting the second law of
thermodynamics The entropy of an isolated system
never decreases. It either stays constant
(reversible processes) or increases (irreversible
processes).
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Order to Disorder
Entropy is a measure of the disorder of a system.
This gives us yet another statement of the second
law Natural processes tend to move toward a
state of greater disorder.
Example If you put milk and sugar in your coffee
and stir it, you wind up with coffee that is
uniformly milky and sweet. No amount of stirring
will get the milk and sugar to come back out of
solution.
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Order to Disorder
Another example When a tornado hits a building,
there is major damage. You never see a tornado
approach a pile of rubble and leave a building
behind when it passes. Thermal equilibrium is a
similar processthe uniform final state has more
disorder than the separate temperatures in the
initial state.
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Unavailability of Energy Heat Death
Another consequence of the second law In any
natural process, some energy becomes unavailable
to do useful work.
If we look at the universe as a whole, it seems
inevitable that, as more and more energy is
converted to unavailable forms, the ability to do
work anywhere will gradually vanish. This is
called the heat death of the universe.
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Statistical Interpretation of Entropy and the
Second Law
Microstate a particular configuration of
atoms Macrostate a particular set of macroscopic
variables This example uses coin tosses
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Statistical Interpretation of Entropy and the
Second Law
Similarly, the most probable distribution of
velocities in a gas is Maxwellian
The most probable state is the one with the
greatest disorder, or the greatest entropy. With
k being Boltzmanns constant and W the number of
microstates,
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Statistical Interpretation of Entropy and the
Second Law
Free expansionstatistical determination of
entropy. Determine the change in entropy for the
adiabatic free expansion of one mole of a gas as
its volume doubles. Assume W, the number of
microstates for each macrostate, is the number of
possible positions.
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Statistical Interpretation of Entropy and the
Second Law
In this form, the second law of thermodynamics
does not forbid processes in which the total
entropy decreases it just makes them exceedingly
unlikely.
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Thermodynamic Temperature Third Law of
Thermodynamics
Since the ratio of heats exchanged between the
hot and cold reservoirs in a Carnot engine is
equal to the ratio of temperatures, we can define
a temperature scale using the triple point of
water T (273.16K)(Q/Qtp). Here, Q and Qtp are
the heats exchanged by a Carnot engine with
reservoirs at temperatures T and Ttp.
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Thermodynamic Temperature Third Law of
Thermodynamics
Also, since the maximum efficiency of a heat
engine is
there is no way to achieve a temperature of
absolute zero. This is the third law of
thermodynamics It is not possible to reach
absolute zero in any finite number of processes.
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Summary

• Heat engine changes heat into useful work
• Efficiency work/heat input
• Maximum efficiency 1 TL/TH
• Refrigerators and air conditioners are heat
  engines, reversed COP heat removed/work
• Heat pump COP heat delivered/work
• Second law of thermodynamics Natural processes
  always tend to increase entropy

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Summary

• Entropy change in reversible process

• Change in entropy gives direction to arrow of
  time
• As time goes on, energy becomes degraded.
• Heat engines cause thermal pollution.