Βασικές Εννοιες Ενέργειας

Εισαγωγή

■ Το λεξιλόγιο της Ενέργειας■ Επισκόπηση μονάδων ■ Βασικές έννοιες Θερμοδυναμικής

■ Σύστημα■ Κατάσταση■ Διεργασία■ Κύκλος

■ Εννοιες Θερμοκρασίας και Κλίμακες Θερμοκρασίας, Πίεσης, Μετρήσεις

Θερμοδυναμική

■Επιστημονική προσέγγυση σε θέματα Ενέργειας και Εντροπίας

■Ενέργεια, έργο, θερμότητηα■Πειραματική επιστήμη■Φορμαλισμός και αξιωματική

περιγραφή, από τον Ηράκλειτο στον Καραθεοδωρή

■Νόμοι

Πρώτος Νόμος – Διατήρηση Ενέργειας

Δεύτερος Νόμος

■ Η Ενέργεια έχει ποιοτικά και ποσοτικά χαρακτηριστικά ■ Ενέχει διεργασίες που μεταβάλουν την ποιότητα της ενέργειας

Μακροσκοπική και Μικροσκοπική Θεώρηση

■ Η ιδιότητητες της ύλης άναφέρονται στη συμπεριφορα των σωματιδίων (μορίων)

■ Ας θεωρήσουμε τη συμπεριφορά ενός αέριου σε ένα δοχείο.

■ Η πίεση του αερίου είναι το αποτέλεσμα της μεταφοράς ορμής των σωματιδίων (μορίων) στο τείχωμα του δοχείου.

■ Ας δούμε την δύναμη που μεταφέρεται σε μια απειροελάχιστη περιοχή του τειχώματος, δηλαδή την πίεση (μικροσκοπική θεώρηση).

■ Ενας μετρητής πίεσης μας αποκαλύπτη την πίεση, την συλλογική δύναμη στο τείχωμα (μακροσκοπική θεώρηση).).

■ Η μακροσκοπική θεώρηση δείχνει την συλλογική συμπεριφορά (Κλασική Θερμοδυναμική).

■ Η μικροσκοπική θεώρηση καταπιάνεται με τις ιδιότητητες της ύλης, του αερίου (Στατιστική Θερμοδυναμική).

■ Η εφαρμοσμένη Θερμοδυναμική μας οδηγεί στην πρακτική αξιοποίηση της ζεύσης του μικροσκοπικού με το μακροσκοπικό επίπεδο

.

Θερμοδυναμικό Σύστημα

■ Τι ακριβώς συμβαίνει? ■ Στη μηχανική, το πρώτο βήμα είναι να

ορίσουμε την κίνηση ενός σώματος βρίσκοντας όλες τις δυνάμεις που το επιρεάζουν (Figure 2).

■ Εφαρμόζουμε τον 2ον Νόμο του Νεύτωνα. ■ Στη θερμοδυναμική, «Σύστημα»

αναφέρεται στο αντικείμενο της ανάλυσης.■ Αφού ορίσουμε το «Σύστημα» βρίσκουμε

τις δυνάμεις και τους σχετικούς Νόμους και σχέσεις

■ Σύστημα – ότι χρειάζεται να μελετήσουμε■ Τα υπόλοιπα είναι το περιβάλλον του Συστήματος. ■ Το Σύστημα ορίζεται από ένα «αμετάβλητο» όριο. ■ Κλειστό Σύστημα και Σύστημα Ελέγχου

Κλειστό Σύστημα (control mass)■ A closed system refers to a fixed quantity of matter.

■ A closed system is used when a particular quantity of matter is under study. ■ A closed system always contains the same matter. ■ There can be no transfer of mass across its boundary. ■ What do we call the system if even energy is not allowed

to cross the boundary?■ The figure shows a gas in a piston-cylinder assembly. ■ Let us consider the gas to be a closed system. ■ The boundary lies just inside the piston and cylinder

walls, as shown by the dashed lines on the figure. ■ If the cylinder were placed over a flame, the gas would

expand, raising the piston. ■ The portion of the boundary between the gas and the

piston moves with the piston. ■ No mass would cross this or any other part of the

boundary.

Ανοιχτό Σύστημα (control volume)

■ An open system (control volume) is a properly selected region in space. ■ It encloses a device that involves mass flow such as nozzle, compressor,

turbine. ■ Flow through such devices is best studied by selecting the region within

the device as the control volume . ■ Both mass and energy can cross the boundary of the control volume. ■ There are no concrete rules for the selection of the control volume but

proper choice makes the analysis much easier .■ The boundary of the control volume is called boundary surface■ The boundary surface can be real or imaginary■ A control volume can be fixed in shape and size or it may involve a

moving boundary.

Ανοιχτό Σύστημα

Ανοιχτό Σύστημα

Ιδιότητες■ To describe a system and predict its

behavior requires knowledge of its properties and how those properties are related.

■ Properties are macroscopic characteristics of a system.

■ Any characteristic of a system is called a property. Some familiar properties are pressure P, temperature T, volume V, and mass m.

■ Properties describe the state of a system only when the system is in an equilibrium state.

■ Not all properties are independent. Density is a dependent property on pressure and temperature.

Πυκνότητα ως ιδιότητα■ Density is mass per unit volume;■ = mass/volume (kg/m3)

■ Specific gravity: the ratio of the density of a substance to the density of some standard substance at specified temperature (usually water at 4 oC)

■ Specific volume is volume per unit mass.■ = Volume/mass, (m3/kg)■ = 1/

r

P

Gases

T

Gases

Volume r

P

Liquids

r

T

Liquids

Water

Εξωτερικές και εσωτερικές ιδιότητες

■ Intensive properties are those that are independent of the size of system, such as temperature, pressure, and density.

■ Extensive properties are dependent on the size (or extent) of the system. Mass m, volume V, and total energy E are some examples of extensive properties.

■ Criteria to differentiate extensive and intensive properties is illustrated in the Figure.

■ Extensive properties per unite mass are called specific properties (i.e. specific volume).

Κατάσταση Συστήματος

■ A state is defined as a condition of a substance that can be described by certain observable macroscopic properties. (T, P, , etc.)

■ In above figure, the system does not undergo any change. All properties can be measured throughout the system. Hence the condition of the system is completely described. This condition is called state 1.

■ Now remove some weights. If the value of even one property changes, then the state will change to different one (state 2).

■ The word State refers to the condition of a system as it is described by its properties.

State 1

m = 2kgT1= 20 °CV1= 1.5 m3

m = 2kgT1= 20 °CV1= 2.5 m3

State 2

Ισοροπία

■ Thermodynamics deals with equilibrium states.

■ The word equilibrium implies a state of balance.

■ Equilibrium state means that there are no unbalanced potentials (or driving forces) within the system.

■ A system is said to be in thermodynamic equilibrium if it maintains thermal, mechanical, phase, and chemical equilibrium.

Θερμοδυναμική Ισοροπία

■ Thermal equilibrium means that there is no temperature differential through the system.

20 °C 30 °C

30 °C

35 °C 40 °C

No thermal equilibrium

32 °C

32 °C 32 °C

32 °C

32 °C

Thermal equilibrium

Μηχανική Ισοροπία

■ Mechanical equilibrium means that there is no change in pressure in the system.

(a) Slow compression (quasi-equilibrium)

20 pa 20 pa

20 pa

20 pa 20 pa

(b) fast compression (non quasi-equilibrium)

20 pa

20 pa

90 pa

Ισοροπία Φάσεως

■ Phase equilibrium means that the mass of each phase reaches an equilibrium level and stays there.

Water

Vapor, P > 0

After some time

Water

Vapor, P = Pv

After long time

Water

Vacuum t= 0, P = 0

At t = 0

Χημική Ισοροπία

■Chemical equilibrium means that the chemical composition of the system does not change with time

Κατάσταση

■ We mentioned earlier that a state is described uniquely by measuring a few of its properties. The remaining properties will assume certain values. The question here is how much is this “few”?.

■ The answer depends on how simple or complex our system is.

■ If we have a system where the gravitational, electrical, magnetic, motion and surface tension effects are absent, then this system is called a simple compressible system.

■ According to what is called “state postulate”, the number of properties required to completely specify the state of such system is two independent, intensive properties.

Κατάσταση

■ If, however, the gravitational effects are important in the simple compressible system, then the elevation z needs to be specified in addition to the two properties necessary to fix the state.

■ The state postulate requires that the two properties are independent of each other.

■ Two properties are considered to be independent if one property is varied while the other one is constant.

■ Temperature and specific volume are good examples. ■ You will see, however, in coming units that temperature and

pressure are not always independent of each other. They become dependent during phase change processes.

Κύκλοι και Διεργασίες

■ Any change from one equilibrium state to another is called a process.

■ Process diagrams are very useful in visualizing the processes.

■ The series of states through which a system passes during a process is called a path

■ To describe a process completely initial and final states as well as the path it follows, and the interactions with the surrounding should be specified

■ A process with identical end states is called a cycle

■ Process diagrams plotted by employing thermodynamic properties as coordinates are very useful in visualizing the processes.

■ Isothermal process means a process at constant T.

■ Isobaric process means a process at constant pressure

■ Isochoric process means a process at constant volume

Ημι-Ισοροπία■ During a quasi-static or quasi-equilibrium

process, the system remains infinitesimally close to an equilibrium state at all times.

■ A sufficiently slow process that allow the system to adjust itself internally so that properties in one part of the system do not change any faster than those at other parts.

■ Compression is very slow and thus equilibrium is attained at any intermediate state. Therefore, the intermediate states can be determined and process path can be drawn.

■ It is an idealized process but many process closely approximate it with negligible error.

■ Quasi-Equilibrium, Work-Producing Devices Deliver the Most Work (it is the standard to which other processes can be compared) (a) Slow compression (quasi-equilibrium)

20 pa 20 pa

20 pa

20 pa 20 pa

State 1

State 2 Process path

P

V

Intermediate states

20

Διεργασίες σε μή-Ισοροπία

■ Compression process is fast and thus equilibrium can not be attained.

■ Intermediate states can not be determined and the process path can not be defined. Instead we represent it as dashed line.

(b) Fast compression (non quasi-equilibrium)

20 pa

20 pa

90 pa

State 1

State 2P

V

Non-equilibruim process

20

90

?

Μορφές Ενέργειας

■ In absence of magnetic, electric, and surface tension effects, the total energy of a system consists of the kinetic, potential, and internal energies and is expressed as

■ The macroscopic form of energy are those a system possesses as a whole with respect to some outside reference (i.e. kinetics and potential).

■ The microscopic forms of energy are those related to the molecular structure of the system , independent of outside reference frames (i.e. internal).

■ The change in the total energy E of a stationary system (closed system) is identical to the change in its internal energy U.

(kJ/kg) 2

basis massunit aon or,

(kJ), 2

(kJ),

2

2

gzv

upekeue

mgzmv

mume

PEKEUE

Μορφές Ενέργειας (συν.)The portion of the internal energy of a system associated

with the

1. kinetic energies of the molecules is called the sensible energy.

2. phase of a system is called the latent energy.

3. atomic bonds in a molecule is called chemical energy.

4. strong bonds within the nucleus of the atom itself is called nuclear energy.

5. Static energy (stored in a system)

6. Dynamic energy: energy interactions at the system boundary (i.e. heat and work)

kgkJeU /1073.6 10235

Θερμοκρασία

■ The zeroth law of thermodynamics states that: If two bodies are in thermal equilibrium with the third body, they are also in thermal equilibrium with each other.

■ The equality of temperature is the only requirement for thermal equilibrium.

Κλίμακες Θερμοκρασίας

■ I n thermodynamics it is desirable to have a temperature scale that is independent of the properties of any substance.

■ Note: it makes no difference to use K or C in formulas involving temperature difference. However, you should use Absolute temperature in formulas involving temperature only like the ideal gas low.

FTRT

CTKT

CTFT

KTRT

FTRT

CTKT

o

o

oo

o

o

328.1

8.1

67.459

15.273

Μετρήσεις

The seven fundamental dimensions and their

units in SI (International System).

Μετρήσεις

SI British System Conversion

Length Meter (m) Foot (ft) 1 ft = 0.3048 m

Time Second (s) Second (s)

Mass

Kg

Slug Pound mass (lbm) 1 slug = 32.2 lbm

1 slug =14.59 kg 1 lbm = 0.4536 kg

Force

Newton (N) 1 N = (1Kg).(1 m/s2)

Pound force (lbf) 1 lbf = (1 slug)(1. ft/s2)

1 lbf = 4.448 N

Definition of

Unit force

Newton (N): is the force required to give a mass of 1 kg an acceleration of 1 m/ s2.

Pound force (lbf) is the force required to give a mass of 1 slug an acceleration of 1 ft/ s2.

°C = (5/9)*(°F –32)

°R = (9/5)*K

Tempe-rature

Degree Celsius.(°C) Absolute Temp.: Kelvin (K).

K = °C + 273.15

Degree Fahrenheit (°F) Absolute Temp.: Rankine (°R)

°R = °F + 459.67

°C = (5/9)*(°F –32)

°R = (9/5)*K

Πίεση

Pressure is defined as the force exerted by a fluid per unit area. Units in SI are Pa=N/m2. The pressure unit Pascal is too small for pressure encountered in practice.

Therefore, kPa and MPa are commonly used.

Units in British are : psf = lbf/ft2, psi = lbf/in2

You have to convert from psi to psf ( 144 in2 = 1 ft2)

psibarskPaPaatm

kPaMPaPabar

696.1401325.1325.101325,1011

1001.0101 5

Πίεση (συν.)

Absolute pressure, is measured relative to absolute vacuum (i.e., absolute zero pressure.)

Gauge pressure, is measured relative to atmospheric pressure

atmabsatmvac

atmatmabsgage

PPPP

PPPP

below pressurefor

above pressurefor

Πίεση (συν.)

Variation of Pressure with Depth

The pressure variation in a constant density fluid is given as

P + Z = constant Or P1+ Z1 = P2 + Z2

Z is the vertical coordinate ( positive upward). is the specific weight of fluids, (N/m3)

For small to moderate distances, the variation of pressure with height is negligible for gases because of their low density.

gr

ΠίεσηPressure at a Point• The pressure at a point in a fluid has the same

magnitude in all direction.

Πίεση (συν.)Pressure Variation in horizontal planes

Pressure is constant in horizontal planes provided the fluid does not change. ( this leads to Pascal’s principle.)

. 1

2

1

2

2

2

1

121 A

A

F

F

A

F

A

FPP

Noting that P1 = P2, the area ratio A2/A1 is called the ideal mechanical advantage. Using a hydraulic car jack with A2/A1 = 10, a person can lift a 1000-kg car by applying a force just 100 kg (= 908 N).

Πιεσόμετρο

A device based on P + Z = constant is called a manometer (Right), and it is commonly used to measure small and moderate pressure differences.

w

f

w

f

w

f

s g

g

rr

rr

r S

Specific gravityP2 = Patm + h

FIGURE 1–61Schematic for Example 1–8.

1-17

Βαρόμετρο και Ατμοσφαιρική Πίεση

• The atmospheric pressure is measured by a device called a barometer; thus the atmospheric pressure is often referred to as the barometric pressure.

0

( )

B B C C

C vapor

B atm C B

Hg

P Z P Z

P P

P P Z Z

gh

r

• The standard atmospheric pressure is the pressure produced by a column of mercury 760 mm in height at 0oC. The unit of mmHG is also called the torr in honor of Evangelista Torricelli (1608−1647).

• The atmospheric pressure at a location is simply the weight of the air above that location per surface area. Patm

changes with elevation and weather conditions.

The length or the cross-sectional area of the tube has no effect on the height of the fluid column of a barometer.

kPaPkPaP

kPaPkPaP

Patorr

kPatorrmmHgP

mm

Denvermm

atm

5.26;05.54

4.83;88.89

3.1331

325.101760

000,105000

:16101000

Βαρόμετρο και Ατμοσφαιρική Πίεση

Τεχνική Επίλυσης Προβλημάτων

Step-by-step approach:1. Problem Statement2. Schematic3. Assumptions4. Physical Laws5. Properties6. Calculations

7. Reasoning, Verification, and Discussion

The assumptions made while solving an engineering problem must be reasonable and justifiable.

Τεχνική Επίλυσης Προβλημάτων

A result with more significant digits than that of given data falsely implies more accuracy.

When solving problems, we will assume the given information to be accurate to at least 3 significant digits. Therefore, if the length of a pipe is given to be 40 m, we will assume it to be 40.0 m in order to justify using 3 significant digits in the final results.