The Second Law of Thermodynamics

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The Second Law of Thermodynamics

• Cengel Boles, Chapter 5

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The Second Law of Thermodynamics

• So far we have studied
• conservation of energy (i.e., First Law of
  Thermodynamics)
• conservation of mass
• tabulated thermodynamic properties and equations
  of state (e.g., ideal gas law)
• There is a need for another law one that tells
  us what sort of processes are possible while
  satisfying conservation principles

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Second Law Statements

• Like the 1st Law, the 2nd Law of Thermodynamics
  is based upon a long history of scientific
  experimentation
• There is no single verbal or math statement for
  this Law - instead, there is a collection of
  statements, deductions, and corollaries regarding
  thermodynamic processes that together form the
  2nd Law
• Two popular statements
• Clausius statement
• Kelvin-Planck statement

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Kelvin-Planck Statement

• It is impossible for any device that operates as
  a cycle to receive heat from a single thermal
  reservoir and produce an equivalent amount of
  work

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Clausius Statement

• It is impossible to construct a device that
  operates as a cycle whose sole effect is the
  transfer of heat from a lower temper-ature
  reservoir to a higher temperature reservoir

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Thermodynamic Cycles

• Cycle energy balance
• Types of cycles
• heat engines, (aka power cycles)
• refrigeration and heat pump cycles

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Heat Engines

• Net (cycle) work output
• Thermal efficiency

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Refrigeration Heat Pump Cycles

• Net work input
• Coefficient of performance (COP)

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Reversible Processes

• Reversible Process a process that can be
  reversed, allowing system and surroundings to be
  restored to their initial states
• no heat transfer
• no net work
• e.g., adiabatic compression/expansion of a gas in
  a frictionless piston device

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Reversible Processes, cont.

• Reversible processes are considered ideal
  processes no energy is wasted, i.e., all
  energy can be recovered or restored
• they can produce the maximum amount of work
  (e.g., in a turbine)
• they can consume the least amount of work (e.g.,
  in a compressor or pump)
• they can produce the maximum KE increase (e.g.,
  in a nozzle)
• when configured as a cycle, they produce the
  maximum performance (i.e., the highest ?th or COP)

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Irreversible Processes

• Irreversible Process - process that does not
  allow system and surroun-dings to be restored to
  initial state
• such a process contains irreversibilities
• all real processes have irreversibilities
• examples
• heat transfer through a temperature difference
• unrestrained expansion of a fluid
• spontaneous chemical reaction
• spontaneous mixing of different fluids
• sliding friction or viscous fluid flow
• electric current through a resistance
• magnetization with hysteresis
• inelastic deformation

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Internally Reversible Processes

• A process is called internally reversible if no
  irreversibilities occur within the boundary of
  the system
• the system can be restored to its initial state
  but not the surroundings
• comparable to concept of a point mass,
  frictionless pulley, rigid beam, etc.
• allows one to determine best theoretical
  performance of a system, then apply efficiencies
  or correction factors to obtain actual
  performance

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Externally Reversible Processes

• A process is called externally reversible if no
  irreversibilities occur outside the boundary of
  the system
• heat transfer between a reservoir and a system is
  an externally reversible process if the outer
  surface of the system is at the reservoir
  temperature

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The Carnot Principles

• Several corollaries (the Carnot principles) can
  be deduced from the Kelvin-Planck statement
• the thermal efficiency of any heat engine must be
  less than 100
• ?th of an irreversible heat engine is always less
  than that of a reversible heat engine
• all reversible heat engines operating between the
  same two thermal reservoirs must have the same
  ?th

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The Kelvin Temperature Scale

• Consider a reversible heat engine operating
  between TH and TL
• Kelvin proposed a simple relation

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The Kelvin Temperature Scale, cont.

• Kelvins choice equates the ratio of heat
  transfers in a reversible heat engine to a the
  ratio of absolute temperatures
• Need a reference to define the magnitude of a
  kelvin (1 K) - the triple point of water is
  assigned 273.16 K

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Maximum Performance of Cycles

• Carnot Heat Engine
• Carnot Refrigerator
• Carnot Heat Pump

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The Carnot Cycle

• The Carnot cycle is the best-known reversible
  cycle, consisting of four reversible processes
• adiabatic compression from temperature TL to TH
• isothermal expansion with heat input QH from
  reservoir at TH
• adiabatic expansion from temperature TH to TL
• isothermal compression with heat rejection QL to
  reservoir at TL

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The Carnot Cycle, cont.

• Note
• the heat transfers (QH , QL) can only be
  reversible if no temperature difference exists
  between the reservoir and system (working fluid)
• the processes described constitute a power cycle
  it produces net work and operates clockwise on a
  P-v diagram
• The Carnot heat engine can be reversed (operating
  counter-clockwise on a P-v diagram) to become a
  Carnot refrigerator or heat pump
• the thermal efficiency and coefficients of
  performance of Carnot cycles correspond to
  maximum performance