General Concepts for Development of Thermal Instruments

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General Concepts for Development of Thermal
Instruments

• P M V Subbarao
• Professor
• Mechanical Engineering Department

Scientific Methods for Construction of
Instruments !!!
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Definition of An Instrument

• A tool required for quantitative description of a
  thermodynamic system.
• Capable to reach any one of the following
  equilibrium with a system.
• Thermal Equilibrium
• Mechanical Equilibrium
• Chemical Equilibrium

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Basic Steps in Development of Instruments

• Development of Mathematical Model for
  Identification of Parameters to be measured.
• Identification of characteristics to be
  possessed by a general Instruments.
• Qualitative and Quantitative models for
  determination of Instrument design details.
• Selection of geometrical and physical parameters.

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Theory of Heat

• Written by Maxwell and published first in 1870
• Describes his views of the limitations of the
  Second Law of Thermodynamics
• Maxwell Relations were first introduced in this
  book

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Why Use Maxwell Relations?

• Certain variables in thermodynamics such as
  entropy, are hard to use in practice.
• Maxwell relations provide a way to exchange
  variables

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Characterization of Working Fluid
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Constant Pressure Heating Process
Vapour
Liquid Vapour
h
Liquid
s
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Constant Pressure Heating Process
s
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Analysis of Constant Pressure Steam Generation
Specific Specific Specific
Pressure Enthalpy Entropy Temp Volume
MPa kJ/kg kJ/kg/K C m3/kg
1 1 3500 7.79 509.9 0.3588
2 5 3500 7.06 528.4 0.07149
3 10 3500 6.755 549.6 0.03562
4 15 3500 6.582 569 0.02369
5 20 3500 6.461 586.7 0.01776
6 25 3500 6.37 602.9 0.01422
7 30 3500 6.297 617.7 0.01187
8 35 3500 6.235 631.3 0.0102
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Behavior of Fluid At Increasing Pressures
All these show that the sensitivity of the fluid
increases with increasing pressure.
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Ideal Rankine Cycle p-h Diagram
3
2
1
4
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Ideal Rankine Cycle P-h Diagram
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What are some examples of Maxwell Relations?
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Using Maxwell Relations
Maxwell Relations can be derived from basic
equations of state, and by using Maxwell
Relations, working equations can be derived and
used when dealing with experimental data.
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Description of A System

• Description of a system is essential for Thermal
  Analysis.
• Microscopic Description or Macroscopic
  Description.
• Microscopic Description
• A System consists of a Substance.
• A collection of atoms or molecules.
• Each Atom can be described by its position,
  velocity, mass.
• Collective description of atoms is the
  description of System.
• Each atom requires three equations for the
  description of position and three equations for
  the description of velocity.
• Millions of equations !
• Highly computationally intensive.
• Kinetic Theory and Statistical Mechanics use
  Probability Theory.
• This is a true description of system but
  impractical.

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Macroscopic Description of A System

• Thermal Engineering uses Macroscopic Description
  of a system.
• Gross or average effects of many molecules are
  described and measured.
• These effects are perceived by our senses and
  measured by instruments.
• This description is the time-averaged influence
  of many molecules.
• A Virtual Description of a System but truly
  practicable.

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What do we measure to describe a System?

• LENGTH (m)
• AREA (sq. m)
• VOLUME (cu. m)
• TIME (s, min, h)
• VELOCITY (m/s)
• ACCELERATION (m/s2)
• MASS (kg)
• FORCE or WEIGHT (N)
• PRESSURE (kPa, mm of Hg, m of water)

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Thermodynamic Property

• Any suitable characteristic whose value depends
  on the condition of a system and which is
  relevant to our thermodynamic study is known as
  a Thermodynamic Property.
• Primitive Property -- Directly observable -- With
  simple experiments -- No change in system.
• Derived Property -- Vigorous experiments -- To be
  calculated using observations.
• Intensive property -- Local property --
  Independent of mass or size of the system.
• Extensive property -- depends on the extent of
  the system -- Obey Colligative Law.

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Role of A Thermodynamic Property

• Suppose you want to forecast the weather this
  weekend in New Delhi.
• Identify true characteristics of weather which
  can be used to understand and define the state of
  weather.
• Say Temperature.
• Is the Temperature is a true characteristic of
  weather condition.
• You construct a formula for the temperature as a
  function of several environmental (measurable)
  variables.
• Now you would like to see how your weather
  forecast would change as one particular
  environmental factor changes, holding all the
  other factors constant.
• Will this temperature, truly represent the state
  of the weather?
• Is the Temperature A Property of Weather?
• To do this investigation, you would use the
  concept of a partial derivative...

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Corollaries on Properties.

• Corollary 1 A change of state is fully described
  by means of the initial and final values of all
  the primitive properties of the system.
• A change occurs when at least one of its
  primitive properties changes value.
• Corollary 2 A process is required for the
  determination of a derived property.
• Corollary 3 The change in value of a property
  is fixed by the end states of a system undergoing
  a change of state and is independent of the path.
• Corollary 4 Any quantity which is fixed by the
  end states of a process is a property.
• Corollary 5 When a system goes through a cycle,
  the change in value of any property is zero.
• Corollary 6 Any quantity whose change in a cycle
  is zero is a property of a system.