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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 h s Liquid Liquid +Vapour Vapour

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Constant Pressure Heating Process s h

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Specific PressureEnthalpyEntropyTempVolume MPakJ/kgkJ/kg/KCm3/kg 1135007.79509.90.3588 2535007.06528.40.07149 31035006.755549.60.03562 41535006.5825690.02369 52035006.461586.70.01776 62535006.37602.90.01422 73035006.297617.70.01187 83535006.235631.30.0102 Analysis of Constant Pressure Steam Generation

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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 1 2 3 4

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Ideal Rankine Cycle : P-h Diagram 1 2 3 4 1 2 3 4 1 2 3 4

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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/s 2 ) 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.

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