Thermodynamics

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Thermodynamics

• Chapter 15

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Expectations

• After this chapter, students will
• Recognize and apply the four laws of
  thermodynamics
• Understand what is meant by thermodynamic terms
• Recognize and distinguish among four kinds of
  thermal processes
• Distinguish between reversible and irreversible
  processes

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Expectations

• After this chapter, students will
• Analyze the properties and operations of heat
  engines
• Calculate the changes in entropy associated with
  thermal processes

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Thermodynamics Some Fundamentals

• Thermodynamics is the study of the economy of
  heat energy and mechanical work, in the context
  of the ideal gas.
• Understanding thermodynamic concepts and
  mathematical relationships depends on
  understanding some terms.

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Systems and Their Boundaries

• In mechanics, we introduced the idea of the
  system a user-defined collection of objects.
• In thermodynamics, system still means that.
  However, we add the notion that the system will
  usually include some definite amount of a fluid
  typically, an ideal gas. It might also include
  other elements, such as the fluids container.
  Its always important to be clear about whats in
  the system, and what isnt.

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Systems and Their Boundaries

• Once we have decided what the system is, we can
  say that the surroundings consists of everything
  that isnt the system.
• The system is separated from its surroundings by
  walls. If the walls do not allow heat to pass
  through them, they are adiabatic walls. If heat
  can pass freely through the walls, we call them
  diathermal walls.

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The State of a System

• The characteristics that tell us what we want to
  know about a system define its condition, or
  state.
• If the system consists of some amount of an ideal
  gas, well be interested in the temperature,
  pressure, volume, and mass of the gas. Those
  quantities are the state variables of the system.

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Common Sense 0th Law of Thermodynamics

• Suppose we have three systems A, B, and C.
• Suppose that A is in thermal equilibrium with C.
  Suppose also that B is in thermal equilibrium
  with C.
• Then A is in thermal equilibrium with B, and no
  heat will flow between them if they are in
  contact.
• (C is intended to be a thermometer.)

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Energy Conservation 1st Law of Thermodynamics

• Mathematical statement
• What does this mean?
• DU is the change in the systems internal energy
• Uf is the systems final internal energy
• U0 is the systems initial internal energy
• Q is the heat added to the system
• W is the work done by the system

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Energy Conservation 1st Law of Thermodynamics

• Think of U as being the systems bank balance,
  and think of work and energy and heat as being
  forms of cash. What weve said is that the
  change in the systems balance is its income
  (heat) minus its spending (work).

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Thermal Processes

• A process is how the system, and its
  surroundings, change from one state to another.
• Were going to consider four special cases of
  thermal processes. These special cases help us
  to understand what the laws of thermodynamics
  tell us about systems and their properties.

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Thermal Processes

• In every case, we assume that the process occurs
  slowly. The technical term for occurs slowly
  is quasi-static.
• What does slowly mean? It means that the
  system has time to mix during the process. At
  all times, we consider the temperature and the
  pressure of the system to be uniform (the same in
  all places throughout the system).

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Isobaric Process

• Isobaric the pressure of the system is
  constant.
• The result first
• Why should this be?

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Isobaric Process

• Consider an ideal gas to which heat is added.
• But AS DV Vf Vi

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Isobaric Process

• This process can be represented graphically,
  plotting pressure vs. volume. Notice that the
  work is the area under this plot (P times DV).

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Isochoric Process

• Isochoric the volume of the system is constant.
• The result
• Why? If volume is constant, nothing moves. No
  motion, no work. Any heat added to the system
  only changes its internal energy.

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Isochoric Process

• Pressure-volume plot for an isochoric process
• No area under the plot means no work is done.

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Isothermal Process

• Isothermal the temperature of the system is
  constant. Use the ideal gas equation to write P
  as a function of V
• Because P is not constant,

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Isothermal Process

• The work is still the area under the isotherm
  plot. To calculate it, we integrate

(natural log)
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Adiabatic Process

• In an adiabatic process, no heat enters or leaves
  the system
• Q 0. The First Law becomes
• But, as we learned in chapter 14,
• (for a monatomic ideal gas).

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Adiabatic Process

• If , then
• and
• so

(monatomic ideal gas)
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Adiabatic Process

• Notice that the adiabatic curve is different from
  both isotherms (corresponding to the initial and
  final temperatures).
• Its equation is
• where

specific heat capacity _at_ constant pressure
specific heat capacity _at_ constant volume
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Specific Heat Capacities

• Define a molar specific heat capacity, C, for an
  ideal gas Q C n DT
• First Law
• At constant pressure (isobaric)

(SI units J / molK)
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Specific Heat Capacities

• Substitute for Vi and Vf from the ideal gas
  equation
• For a monatomic ideal gas
• Substitute

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Specific Heat Capacities

• Equate this expression for Q to the one from our
  defining equation for molar heat capacity

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Specific Heat Capacities

• At constant volume (isochoric)

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Specific Heat Capacities

• A couple of things to note
• (for a monatomic ideal gas)

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Second Law of Thermodynamics

• Heat flows spontaneously from regions of higher
  temperature to regions of lower temperature. It
  does not flow spontaneously in the other
  direction.
• Set your cup of hot coffee down on the sidewalk
  tonight. Come back and get it in after a few
  minutes. It wont be hotter.

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Second Law and Heat Engines

• As heat flows from a hotter region to a colder
  one, a device can be constructed that will use
  some of that heat to do mechanical work.
• Such a device is called a heat engine.

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Heat Engines

• A familiar example internal combustion (auto)
  engine.
• Hot reservoir burning fuel-air mixture
• Cold reservoir exhaust gases

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Heat Engines Energy Conservation

• The principle of energy conservation requires

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Heat Engines Efficiency

• Efficiency is defined as the ratio of the work
  done by the heat engine to the input heat it
  receives.
• Efficiency is a dimensionless, unitless ratio.

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Efficiency and Reversibility

• A process is called reversible if both the system
  and its environment can be returned, after the
  process, to exactly the same states they were in
  before the process.

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Efficiency and Reversibility

• No process involving friction is reversible.
• Also, any process in which heat flows
  spontaneously from a hot to a cold reservoir is
  irreversible. The system can be restored to its
  original state, but the work required changes the
  environment further from its original state.

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Carnots Principle

• No irreversible heat engine operating between two
  reservoirs at constant temperatures can be more
  efficient than a reversible engine operating
  between the same temperatures. All reversible
  engines operating between the same two
  temperatures have the same efficiency.

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Sadi Nicolas Leonard Carnot

• 1796 1832
• French military engineer

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Efficiency of a Carnot Engine

• If a thermodynamic temperature scale is correctly
  defined, the ratio of the heat into the cold
  reservoir to the heat from the hot reservoir is
  equal to the ratio of the reservoir temperatures
• Lord Kelvin defined his thermodynamic temperature
  scale so that this is true. The temperatures in
  the above equation must be absolute (in Kelvins).

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Efficiency of a Carnot Engine

• Earlier, we said that the efficiency of a heat
  engine is
• Substituting from the previous equation
• This is true for a Carnot engine. Notice that we
  are assuming that the reservoir temperaures are
  not changed by the operation of the engine.

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A Different Kind of Reversibility

• A heat engine diverts some of the heat flowing
  spontaneously from hot to cold, and uses it to
  generate output work.
• If we are willing to input work, then we can
  cause heat to flow from cold to hot. (Heat pump,
  refrigerator.) Notice that this reverse
  operation is not the same thing as thermodynamic
  reversibility.

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Heat Pumps and Refrigerators

• Conservation of energy applies to heat pumps as
  well as to heat engines QH W QC
• For a thermodynamically-reversible heat pump or
  refrigerator
• Refrigerator coefficient of performance

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Entropy

• Entropy the loss of our ability to use heat to
  perform work, because of the irreversible
  spontaneous flow of heat from higher to lower
  temperatures.
• If heat flows into or out of a system reversibly,
  the systems change in entropy is

SI units J / K
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Entropy and Reversible Engines

• The change in entropy associated with the
  operation of a Carnot engine
• hot reservoir cold
  reservoir
• total change

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Entropy and Reversible Engines

• But Carnots principle said that
• So, the total change in entropy associated with
  the operation of a Carnot engine is
• So the operation of a reversible engine does not
  change the total entropy of the universe.
  Irreversible processes increase the entropy of
  the universe.

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Energy Unavailable for Doing Work

• Consider a reversible engine working between
  reservoir temperatures of 650K and 150K.
• Its efficiency
• If 1200 J of heat are drawn from
• the hot reservoir, the work is

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Energy Unavailable for Doing Work

• Now we provide a path for our 1200 J of heat to
  flow irreversibly from the 650K reservoir to a
  cooler one, at 350K. Now our engines efficiency
  becomes

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Energy Unavailable for Doing Work

• At this decreased efficiency, the work done by
  this 1200 J of heat is
• The work done by this heat in descending from 650
  K to 150 K has decreased by 923 J 685 J, or 238
  J.

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Energy Unavailable for Doing Work

• We can also calculate this loss of work by
  calculating the increase in the entropy of the
  universe associated with the irreversible part of
  the heat flow

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Energy Unavailable for Doing Work

• Then apply Eq. 15.19 from your textbook to
  calculate the energy unavailable for work
• The irreversible flow causes this.