Laws of Thermodynamics

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Laws of Thermodynamics

• Thermal Physics, Lecture 4

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Internal Energy, U

• Internal Energy is the total energy in a
  substance, including thermal, chemical potential,
  nuclear, electrical, etc.
• Thermal Energy is that portion of the internal
  energy that changes when the temperature changes

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Heat, Q

• The flow of energy into or out of a substance due
  to a difference in temperature.
• It results in a loss or gain in the Thermal Energy

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Work, W

• The flow of energy into or out of a substance
  that is NOT due to a difference in temperature.
• It results in a loss or gain in the Internal
  Energy

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First Law

• The first law of thermodynamics states that the
  internal energy of a system is conserved.
• Q is the heat that is added to the system
• If heat is lost, Q is negative.
• W is the work done by the system.
• If work is done on the system, W is negative

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Example using First Law

• 2500 J of heat is added to a system, and 1800 J
  of work is done on the system. What is the change
  in the internal energy of this system?
• Signs Q2500 J, W -1800 J

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Thermodynamic Processes

• We will consider a system where an ideal gas is
  contained in a cylinder fitted with a movable
  piston

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Isothermal Processes

• Consider an isothermal process iso same, so
  isothermal process happens at the same
  temperature.
• Since PVnRT, if n and T are constant then PV
  constant

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Isothermal Processes

• We can plot the pressure and volume of this gas
  on a PV diagram
• The lines of constant PV are called isotherms

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Isothermal Processes

• For an ideal gas, the internal energy U depends
  only on T, so the internal energy does not
  change.
• Q must be added to increase the pressure, but the
  volume expands and does work on the environment.
• Therefore, QW

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Adiabatic Processes

• In an adiabatic process, no heat is allowed to
  flow into or out of the system.
• Q0
• Examples
• well-insulated systems are adiabatic
• very rapid processes, like the expansion of a gas
  in combustion, dont allow time for heat to flow
  (Heat transfers relatively slowly)

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Adiabatic Processes
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Isobaric Processes

• Isobaric processes happen when the pressure is
  constant

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Isovolumetric Processes

• Isovolumetric processes happen when the volume is
  constant

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Calculating Work

• For our ideal gas undergoing an isobaric process

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Calculating Work

• What if the pressure is not constant?
• The work is the area under the curve of the PV
  diagram.

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Adiabatic Process

• Stretch a rubber band suddenly and use your lips
  to gauge the temperature before and after.

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Summary of Processes

• Isothermal T is constant and QW since ?U0
• Isobaric P is constant and WP?V
• Isovolumetric V is constant so W0 and Q ?U
• Adiabatic Q0 so ?U -W

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Example

• An ideal gas is slowly compressed at constant
  pressure of 2 atm from 10 L to 2 L. Heat is then
  added to the gas at constant volume until the
  original temperature is reached. What is the
  total work done on the gas?

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Example
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Example (15-5 in textbook)

• Work is area under the graph.
• Convert pressure to Pa and Volume to cubic meters.

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Example (15-5 in textbook)

• How much heat flows into the gas?

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Example 2 Boiling Water

• 1 kg (1 L) of water at 100 C is boiled away at 1
  atm of pressure. This results in 1671 L of steam.
  Find the change in internal energy.

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Example 2 Boiling Water
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Engines and Refrigerators

• system taken in closed cycle ? ?Usystem 0
• therefore, net heat absorbed work done
• QH - QC W (engine)
• QC - QH -W (refrigerator)

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Heat Engine Efficiency
The objective turn heat from hot reservoir into
work The cost waste heat 1st Law QH -QC
W efficiency e ? W/QH
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Heat Engine

• 1500 J of energy, in the form of heat, goes into
  an engine, which is able to do a total of 300 J
  of work. What is the efficiency of this engine?
• What happens to the rest of the energy?

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Heat Engine

• Can you get work out of a heat engine, if the
  hottest thing you have is at room temperature?
• A) Yes B) No

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Refrigerator
The objective remove heat from cold
reservoir The cost work 1st Law QH W QC
coeff of performance Kr ? QC/W
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New concept Entropy (S)

• A measure of disorder
• A property of a system (just like p, V, T, U)
  related to number of number of different states
  of system
• Examples of increasing entropy
• ice cube melts
• gases expand into vacuum
• Change in entropy
• ?S Q/T
• gt0 if heat flows into system (Qgt0)
• lt0 if heat flows out of system (Qlt0)

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Second Law of Thermodynamics

• The entropy change (Q/T) of the
  systemenvironment is always greater than zero
  (positive)
• never lt 0
• Result order to disorder
• Consequences
• A disordered state cannot spontaneously
  transform into an ordered state
• No engine operating between two reservoirs can be
  more efficient than one that produces 0 change in
  entropy. This is called a Carnot engine

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Carnot Cycle

• Idealized (Perfect) Heat Engine
• No Friction, so DS Q/T 0
• Reversible Process
• Isothermal Expansion
• Adiabatic Expansion
• Isothermal Compression
• Adiabatic Compression

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Perpetual Motion Machines?
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Carnot Efficiency

• The absolute best a heat engine can do is given
  by the Carnot efficiency

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Carnot Efficiency

• A steam engine operates at a temperature of 500
  ?C in an environment where the surrounding
  temperature is 20 ?C. What is the maximum
  (ideal) efficiency of this engine?
• What is the operating temperature were increased
  to 800 ?C ?

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Engines and the 2nd Law
The objective turn heat from hot reservoir into
work The cost waste heat 1st Law QH -QC
W efficiency e ? W/QH W/QH 1-QC/QH
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Summary

• First Law of thermodynamics Energy Conservation
• Q DU W
• Heat Engines
• Efficiency 1-QC/QH
• Refrigerators
• Coefficient of Performance QC/(QH - QC)
• Entropy DS Q/T
• 2nd Law Entropy always increases!
• Carnot Cycle Reversible, Maximum Efficiency e
  1 Tc/Th