ME312 Chapter 1 - Basics PDF

Preview

Summary

Download ME312 Chapter 1 - Basics PDF

Description

5/23/2017

Dr. Christopher Depcik

Prof. Christopher Depcik University of Kansas Department of Mechanical Engineering

Dr. Christopher Depcik

Outline  System and Surroundings  Properties  Density, Pressure, (Velocity), and Temperature  (ME 510) Concepts  State and Process  Units ME 312: 1-2

1

5/23/2017

Dr. Christopher Depcik

Dr. Christopher Depcik

Introduction  The system is what will be

studied in the thermodynamic analysis within this class  The surroundings are everything external to this system  The system is separated from the surroundings by a defined boundary http://www.wiley.com/college/moran/0470495901/animations/system _types/system_types.html

An illustration of a tank defining the system under study and the surroundings external to the system. The boundary illustrates the delineation between the system and surroundings. MSBB – p. 7

ME 312: 1-4

2

5/23/2017

Dr. Christopher Depcik

Closed System  In this specific instance, mass

is constant within the system  However, there can be work and heat added/subtracted (discussed in next chapter) to the system via external means to change the properties within the system  This heat and work can occur through mechanical, electrical, thermal, or other phenomena Even though the boundary of a closed system may change, the mass is still constant as no mass is entering or exiting the system. http://www.wiley.com/college/moran/0470495901/animations/system _types/system_types.html

ME 312: 1-5

MSBB – p. 6

Dr. Christopher Depcik

Example of a Closed System  In an internal combustion engine, the

chemical energy within the fuel is converted to high temperatures and pressures through combustion  The pressure generated then pushes down on the piston creating work (moving boundary work); whereas, the high temperatures created cause heat transfer to the walls  Mass is constant throughout this process, but heat and work are crossing the boundary

http://users.yumaed.org/~tpinnt/cap/CAP_aerospace/SSG_1.HT M

System boundary Moving boundary work

Imagine that you have taken the cross-cut of an engine cylinder. The valves are closed and mass is assumed to be constant after the combustion event. High temperatures and pressures cause heat transfer and boundary work, respectively. MSBB – p. 7

ME 312: 1-6

3

5/23/2017

Dr. Christopher Depcik

Isolated System  Special type of a closed system in which    

there is no heat or work transferred across the boundary Hence, there is no interaction with the surroundings This does not mean necessarily that nothing is happening For example, imagine right after food dye is dropped into water The mass is constant within the system; however, diffusion of the dye will happen (concentration & temperature gradients if dye is different temperature than water)

http://www.youtube.com/watch?v=Bz02z4GSS0k http://www.wiley.com/college/moran/0470495901/animations/system _types/system_types.html

MSBB – p. 6

After droplet has been added, system is closed; however, there is movement within the isolated system ME 312: 1-7

Dr. Christopher Depcik

Open System  In an open system, mass can now

enter and exit the system

 The system is now called a control

volume; whereas, the boundary is now called a control surface  Of note, the following are often used interchangeably by Dr. D  System ~ Control Volume  Boundary ~ Control Surface  Of note, as mass enters or exits the control volume it brings/carries with it information such as energy and momentum (discussed later) http://www.wiley.com/college/moran/0470495901/animations/system _types/system_types.html

In an open system, the control volume contains the region of interest for analysis. Heat transfer and work can cross the control surface, and now so can mass bringing “information” along with it. MSBB – p. 7

ME 312: 1-8

4

5/23/2017

Dr. Christopher Depcik

Example of Open System

Mass flow (air)

 Most everyone is familiar with a car engine  Air and fuel (mass) enter the control volume

(crossing the control surface)

 Internal combustion happens changing chemical

energy to mechanical energy  Heat liberated from the chemical species increases temperature and pressure  This pressure pushes down on a piston creating mechanical motion  This turns the drive shaft that spins the wheels (crossing the control surface)  Exhaust gas is expelled leaving the control volume (crossing the control surface) MSBB – p. 7

Mass flow (fuel) Shaft work

Mass flow (exhaust) In our closed system example before, we were looking at the combustion event. Imagine if you took a cross-cut of an engine and watched what was happening in the cylinder. In this example, we move our boundary to the entire engine. What enters, what leaves, and what is being generated.

ME 312: 1-9

Dr. Christopher Depcik

5

5/23/2017

Dr. Christopher Depcik

Microscopic vs. Macroscopic  Microscopic: uses statistics in order to analyze the average behavior of particles within the system (or control volume) – aka statistical thermodynamics  Macroscopic: gross or overall behavior of the particles making up the system (or control volume) – aka classical thermodynamics  We measure macroscopic properties in the lab using thermocouples, pressure transducers, and other sensors http://abyss.uoregon.edu/~js/21st_century_sci ence/lectures/l ec05.html

One goal of statistical thermodynamics is perform an analysis on the microscopic level (e.g., atoms) in order to calculate the macroscopic quantities easily measured. This helps provide fundamental insight into the control volume under analysis. MSBB – p. 8

ME 312: 1-11

Dr. Christopher Depcik

Statistical Mechanics  Classical view of the universe is that the fundamental

laws are mechanical in nature, and that all physical systems are therefore governed by mechanical laws at a microscopic level  Precise equations of motion that map any given initial state to a corresponding future state at a later time  There is a disconnection between these laws and everyday life experiences, as we do not find it necessary (nor even theoretically possible) to know exactly at a microscopic level the simultaneous positions and velocities of each molecule while carrying out processes at the human scale  Statistical mechanics is a collection of mathematical tools that are used to fill this disconnection between the laws of mechanics and the practical experience of incomplete knowledge

https://en.wikipedia.org/wiki /Statistical_mechanics https://en.wikipedia.org/wiki /Temperature#Definition_from_statistical_mechanics http://hyperphysics.phy-astr.gsu.edu/Hbase/therm o/temper2.html

Microscopic mechanical laws do not contain concepts such as temperature, heat, or entropy, however, statistical mechanics shows how these concepts arise from the natural uncertainty that arises about the state of a system when that system is prepared in practice. The benefit of using statistical mechanics is that it provides exact methods to connect thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas in classical thermodynamics the only available option would be to just measure and tabulate such quantities for various materials. Statistical mechanics also makes it possible to extend the laws of thermodynamics to cases which are not considered in classical thermodynamics, for example microscopic systems and other mechanical systems with few degrees of freedom. This branch of statistical mechanics which treats and extends classical thermodynamics is known as statistical thermodynamics or equilibrium statistical mechanics.

In statistical mechanics, temperature is defined based on the fundamental degrees of freedom of the components involved

ME 312: 1-12

6

5/23/2017

Dr. Christopher Depcik

Shall We Study Statistical Thermodynamics?

ME 312: 1-13

http://slideplayer.com/slide/6639169/

Dr. Christopher Depcik

Property  Macroscopic characteristic of a

system to which a numerical value can be assigned at a given time without knowledge of the previous behavior of the system  For example, at an instant of time you can specify (or measure) the system’s: pressure, temperature, volume, energy, or mass http://proweatherstation.com/Products/products.htm

Using the example of a weather station, the macroscopic properties it is measuring include the temperature, humidity, and pressure of the ambient air.

MSBB – p. 9

ME 312: 1-14

7

5/23/2017

Dr. Christopher Depcik

Extensive Property  Its value for an overall system is the sum of its value for the parts into which the system is divided  This depends on the size or

A cube measuring 1 m  1 m  1 m has a volume of 1 m3. Let’s say that there is 2 kg of mass in this cube. Both of these values are extensive: V = 1 m3 & m = 2 kg

extent of the system under study (or quantity of substance)  Its value may vary with time, but not position  For example: mass, volume, or energy

Now, let’s say the cube’s volume is 8 m3. In this situation, let’s also say that there is 16 kg of mass in this cube. Both of these values are extensive: V = 8 m3 & m = 16 kg

ME 312: 1-15

MSBB – p. 9

Dr. Christopher Depcik

Intensive Property  This property is independent

From the previous slide for this cube: V = 1 m3 & m = 2 kg

of the size or extent of the system  Its value is not additive  Some examples include pressure, temperature, and density  It may vary from place to place within the system at any moment – function of both position and time

And for this cube: V = 8 m3 & m = 16 kg Using an intensive property called density (discussed later), we find that the gas within both cubes have the same overall density (assume uniform cube)

 MSBB – p. 9

m

2

kg ME 312: 1-16

8

5/23/2017

Dr. Christopher Depcik

Example: Driven Cavity Flow  On this slide, I just want you to understand

Moving Plate

Wall

that the fluid is moving within the cavity  Important items:  The top is a plate that is moving  The other three sides are solid walls  This induces a flow within a cavity because of viscosity (fluid “sticking” to plate and each other)  Hence, you can see the movement of the fluid within the cavity  Classical computational fluid dynamics example

Wall

Wall http://spectral.iitk.ac.in/hpcl/?q=ldc

ME 312: 1-17

Dr. Christopher Depcik

Extensive vs. Intensive  Imagine the image on the right is a cube and    



we have taken a cross-section through the cube for driven cavity flow The volume of the cube is defined (extensive) However, depending on the flow within the cube, temperature of the walls, etc. a temperature profile can be found (intensive) Hence, the volume does not change by position, but the temperature does Now, if we were to change the shape of the cube as a function of time, both the extensive and intensive properties would change Nearly all of the time in this class, we will assume that this cube has average properties in order to simplify the analysis Of note, the scale on the right indicates a multiplier on temperature (imagine the lower left corner is cold and the upper right is hot)

http://www.cham.co.uk/phoenics/d_polis/d_lecs/plant/plan3.htm

MSBB – p. 9

ME 312: 1-18

9

5/23/2017

Dr. Christopher Depcik

Extensive vs. Intensive (Another Example)  In engineering analysis,

it will be critical to keep track of both extensive and intensive properties  Both play a role in the description of the working fluid within the system under analysis

http://www.wiley.com/college/moran/0470495901/animations/ext_int_properties/ext_int_properties.html

MSBB – p. 9

ME 312: 1-19

Dr. Christopher Depcik

10

5/23/2017

Dr. Christopher Depcik

¡Three Amigos!  Density (or specific volume), pressure, and temperature are the three measurable intensive properties that are used quite often in engineering  From a macroscopic perspective, the

description of these properties (and others) is simplified by considering them to be distributed continuously throughout a region (continuum hypothesis)  Hence, when substances are treated as continua, it is possible to speak of their intensive thermodynamic properties “at a point” http://www.rockiesventureclub.org/2013/02/pitch-deck-3/three-amigos/

ME 312: 1-21

MSBB – p. 13

Dr. Christopher Depcik

Continuum Hypothesis?  If you delve far down into the guts of your   



system, you will find that it is not continuous in nature There is space between the molecules you are studying Moreover, there is space within the molecule (or atom) itself However, our big picture view (macroscopic) is at a much larger length scale (> inter-atomic distances); hence, we can safely assume that the substance of the object completely fills the space it occupies Hence, your “point” is sufficient to be considered a continuum

http://abyss.uoregon.edu/~js/21st_centur y_science/lectures/lec05.html http://en.wikipedia.org/wiki/Continuum_mecha nics http://physics.aps.org/featured-arti cle-pdf/10.1103/PhysR evLett.110.213001

MSBB – p. 13

What we perceive as continuous a macroscopic basis is actually discontinuous on the microscopic basis (empty space between atoms and molecules) First ever direct observation of the orbital structure of an atom. Notice the empty space between the nucleus and the electron orbital. ME 312: 1-22

11

5/23/2017

Dr. Christopher Depcik

At any instant, the density at a point is defined as:

Density

m  

 Density is defined by which the smallest volume for the matter can be considered a continuum  Given the small atomic

  lim 

where V  is the smallest volume for which a definite value of the ratio exists (contains enough particles for statistical averages to be significant – macroscopic measurement) Hence, the mass associated with a given volume is determined (in principle) by integration:

length scales, this volume is often small enough to be considered a point in the system (or in the flow)  Since it is intensive, it can vary from point to point within a system http://www.wiley.com/college/moran/0470495901/animations/ ext_int_properties/ext_i nt_properties.html http://www.artinaid.com/2013/04/gravity/

m d And not simply as the product of density and volume (although it is sometimes convenient to use this approach – we do this often) ME 312: 1-23

MSBB – p. 13

Dr. Christopher Depcik

Density at a Point  Another view of the same

concept  For a differential control volume (aka “at a point”) V  is the smallest volume where we can assume continuous fluid properties  Hence, our continuum hypothesis

Fox & McDonald, Introduction to Fluid Mechanics

Density can also be defined equivalently using a differential control volume

m 

  lim  

ME 312: 1-24

12

5/23/2017

Dr. Christopher Depcik

Electrons  Charge can be

treated analogously to density  Therefore, electrons (that have mass) can be part of the continuum hypothesis Electrodynamics of Continua I: Foundations and Solid Media By A. Cemal Eri ngen, Gerard A. Maugin

ME 312: 1-25

Dr. Christopher Depcik

Specific Volume The specific volume is simply the inverse of the density

 The reciprocal of the density is the

specific volume  Volume per unit mass  By analogy, it is an intensive property and may vary from point to point  May see the use of specific volume instead of density  Why? Personal preference http://www.wiley.com/college/moran/0470495901/animations/ ext_int_properties/ext_i nt_properties.html

MSBB – p. 14

v

1



We can then equate the total volume and specific volume through the mass.

Taking our previous cube example with: V = 1 m3 & m = 2 kg. If we want to model the cube as a single entity or average (i.e., one big “point”)



m

2

kg

v

1



3



m

kg ME 312: 1-26

13

5/23/2017

Dr. Christopher Depcik

Pressure – Kinetic Theory of Gases  The molecules of a gas are in constant, random    

motion and frequently collide with each other and the walls of the container These molecules contain mass, momentum, and energy As the gas collides with the walls, it imparts a force perpendicular to the wall The sum of all of these forces divided by the area of the wall is defined as the pressure of the gas For our previous cube example (2 kg of air), using Avogadro's constant we find there is approximately 41025 molecules in the cube (i.e., not an insignificant amount)

http://www.grc.nasa.gov/WWW/k-12/ai rplane/pressure.html http://en.wikipedia.org/wiki/File:Translational_motion.gif

MSBB – p. 14

Illustration of the random motion of molecules colliding

ME 312: 1-27

Dr. Christopher Depcik

Avogadro’s Constant  Recalling from chemistry, the

Avogadro constant is the number of constituent particles (usually molecules) that are contained in the amount of substance given by one mole  It is a proportionality factor that relates the molar mass of a material to its mass: 6.0221408571023 mol-1  Air molecular weight is 28.966 gm/mol; hence, 28.966 gm of air will have 6.022 1023 molecules and 2 kg of air will have 4.158 1025 molecules

http://www.daviddarling.info/encyclopedia/A/Avogadro_constant.html https://en.wikipedia.org/wiki/Avogadro_constant

ME 312: 1-28

14

5/23/2017

Dr. Christopher Depcik

Pressure

F  p  lim  normal   A A  A 

 Expanding pressure to a more general concept (i.e.,

At any instant, the pressure at a point is defined as:



Hence, when we measure the pressure in a box, we are measuring the sum of all of the forces over the area of the box

   

fluids), pressure is an intensive property that is equal to the normal force over the area of interest Similar to the continuum description of density, we can provide an analogous pressure definition Taking our same V as the smallest volume that contains enough particles for statistical averages to be significant – macroscopic measurement Imagine the area of this volume to be A  and that the fluid is at rest Hence, the pressure of the fluid at the specified point is defined as the limit where ...