ME 200 L2: Introduction to ThermodynamicsME 200 L2: Introduction to ThermodynamicsVolume, Pressure, Temperature, Design

and Analysis, Problem Solving

Spring 2014 MWF 1030-1120 AML2 given by Indraneel Sircar

J. P. Gore, Reilly University Chair Professorgore@purdue.edu

Gatewood Wing 3166, 765 494 0061Office Hours: MWF 1130-1230

TAs: Robert Kapaku rkapaku@purdue.edu Dong Han han193@purdue.edu

Resources for our learning• Fundamentals of Engineering Thermodynamics, Moran,

Shapiro, Boettner and Bailey, Seventh Edition. • Read assigned sections before coming to class.• Group class email will be used frequently to

communicate. Also use http://www.purdue.edu/mixable• Class participation welcome and essential.

• Given the size of the class, smaller groups of ~10 students to be formed soon. Special opportunities offered to individual ME200 Peer Mentor to lead a group.

• Other Instructors, T. A. s, Classmates, Organized Learning Groups such as www.purdue.edu/si

• Homework: Submission, grading, and return policies will be announced in the class.

Mass, Specific Volume ( ), Density ()

►Matter is made up of “small,” and “homogeneous,” continua distributed throughout “space.” Homogeneous refers to our choice of defining averaged properties.►When substances are treated as continua, it is possible to speak of their intensive thermodynamic properties “at a point.”►At any instant the density () at a point is defined as (see text book equations 1.6 and 1.7)

V

m

V

m

dVm

vV

m

Vfixedpropertiesotherallholding

V

VV

lim

lim

0

'

|

1

v

Molar Specific Volume ( ), Number of mol (n)

►Avogadro’s Number represents the number of molecules in mass containing one “gram mole” or “mole” or “mol.” ► Av=6.022x1023 #/gram mole. A “kmol,” will have 103 times more #

M

mn

kmolkgormolginweightmolecularisMwhereMvv

//,

Molecular/atomic weights M for substances generally of interest in thermodynamics are in Table A-1: C = 12.01 kg/kmol, O2=32.00 kg/kmol, N2=28.01 kg/kmol. Air is a mixture 1 kmol O2 and 3.76 kmol N2 plus small amounts of CO2, Ar, H2O etc. Equivalent Molecular Weight of air is given as 28.97 kg/kmol in Table A-1, p. 890 of text.

v

Pressure (p)►Pressure within gases is force per unit area

resulting from molecular collisions with a container wall and amongst molecules within a gas.

►Visualize pressure within liquids and solids as a force exerted by neighboring particles and bonds The pressure (p) at the specified point is defined as the limit:

A

Fp Normal

AAlim

'

Pressure Units, Absolute and Gauge Pressure

► SI unit of pressure is the pascal:

1 pascal = 1 N/m2

► Multiples of the pascal are frequently used:

► 1 kPa = 103 N/m2, 1 bar = 105 N/m2, 1 MPa = 106 N/m2

► English units for pressure are:

► pounds force per square foot, lbf/ft2 or pounds force per square inch

“psi”, lbf/in2

►When system pressure is greater than atmospheric pressure, the term gage pressure is used.

p(gage) = p(absolute) – patm(absolute)

(Eq. 1.14)►When atmospheric pressure is greater than system pressure, the term

vacuum pressure is used.

p(vacuum) = patm(absolute) – p(absolute) (Eq. 1.15)

Hydrostatic Pressure

• The pressure throughout an uninterrupted fluid is constant at a fixed depth.

Think about the difference in pressure between points H and I, while we discuss the expressions for hydrostatic pressures.

Pressure Measurement

• We can make use of the change in pressure with elevation in a fluid to measure pressure.

• Examples of devices used to measure pressure are:

manometer barometer

ghpp atm ghpp Mvaporatm

p=patm

g

Cortesy: Office of Basic Energy Sciences, U. S. Department of Energy

Temperature (T)

►If two substances (one warmer than the other) are brought into contact and isolated from their surroundings, they interact thermally with changes in observable properties.►When changes in observable properties cease, the two substances are in thermal equilibrium.►Temperature is a physical property that determines whether the two substances are in thermal equilibrium.► A thermometer is used to measure temperature using a change in a thermometric property of a thermometric substance.

► Liquid-in-glass thermometer►A glass capillary tube connected to a bulb filled with liquid and sealed. Space above liquid occupied by vapor or an inert gas.►As temperature increases, liquid expands and the length (L) of the liquid in the capillary indicates the temperature.►The liquid is the thermometric substance. L is the thermometric property.

►Other types of thermometers: Thermocouples, Thermistors, Radiation thermometers and optical pyrometers

Thermometers for Temperature Measurements

Temperature Scales

ΔTºR = ΔTºF = 1.8 x (ΔTK = ΔTºC)

USE ABSOLUTE TEMPERATURES IN ALL YOUR PROBLEM SOLUTIONS.

T(oC) = T(K) – 273.15 (Eq. 1.17)

T(oF) = T(oR) – 459.67 (Eq. 1.18)

oC and oF Relationship

ΔTºR = ΔTºF = 1.8 x (ΔTK = ΔTºC)

USE ABSOLUTE TEMPERATURES IN YOUR PROBLEM SOLUTIONS BECAUSE THE DIFFERENCES ARE IDENTICAL AND SOME FORMULAE LIKE THE IDEAL GAS LAW REQUIRE TEMPERATURE IN ABSOLUTE UNITS.

T(oC) = T(K) – 273.15 (Eq. 1.17)

T(oF) = T(oR) – 459.67 (Eq. 1.18)

oC

oF

(0, 32)

(100, 212)

(-17.7, 0)

oC oF

-17.7 0

0 32

100 212

-273 -460

(-273, -460)

► Some temperatures and ranges of interest► 0 K is the absolute lower limit of a temperature scale► Ice temperature is 273 K► Boiling point of water at atmospheric pressure is 373 K► Healthy human body temperature ~ 309 K► High fever human body temperature ~ 313 K► Hydrocarbon “yellow flame” temperature 1400 K – 1800 K► Hydrocarbon “blue flame” temperature 1900 K – 2400 K ► Effective solar temperature is considered to be 5500K► Absolute upper limit of temperature is not defined yet but

engineering higher than flame temperature materials is challenging. Materials with porous cooling walls may

be used.

Temperatures of Interest

Engineering Design and Analysis

Engineering Design Engineering Analysis

Recognize (or create) a need and define all requirements and constraints associated with it.

Apply fundamental principles to the functionality of the design.

Select “best design,” criteria: cost, efficiency, size, weight, life.

Conservation of mass, momentum species and energy must be followed.

Consider product life cycle reliability, manufacturability, maintenance, sustainability.

Performance prediction, testing, and suggestion of improvements.

Customer and Business considerations: Aesthetics, appearance, color, customer appeal, first to market, capital.

Limitations based on second law of thermodynamics.

Compatibility with other products, systems, policies.

Evaluate potential for scaling in terms of product size or product volume.

Problem Solving Techniques

A fairly straightforward problem:

•The system is easy to define (only one type).

•There are few basic equations.

Thermodynamics problems are more complicated

Exhaust

Exhaust Plume

Ash

Fuel

Coal/Oil/Natural Gas

Air

Steam

Feed Water

• For example, consider a small portion of a coal/oil/natural gas burning power plant.

• Many interconnected working substances such as fuels, air, exhaust, and ash.

• Many interconnected systems and control volumes

• Additional working substances such as liquid water becoming saturated water, saturated steam, superheated steam etc.

Problem Solving Techniques

Important steps to solve any problem in a systematic manner.•Find: What quantities are of customer interest? Usually dictates the definition of the System.•System: Control mass/control volume choice indicates what mass flow and energy interactions exist.•Basic Equations: Which equations are required to determine quantities of interest (related to Find)•Given: What quantities are known?•Assumptions: Do the number of unknowns and available equations match? Otherwise, you need appropriate simplifications and assumptions.•Solution: Evaluate properties, employ correct units, perform calculation, discuss result(s) if necessary.

►We defined temperature, different scales of specifying temperature and their inter-relations.►We summarized temperatures of engineering interest.► We identified the reasons behind the complexity of

thermodynamics problems and defined a methodology for solutions. ► We are ready to do some example problems in class.

Summary