lecture+notes+1+including+fluid+properties+and+annotations

8/14/2019 Lecture+Notes+1+Including+Fluid+Properties+and+Annotations

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Lecture 1: Brief Review of Thermodynamics 1


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Exergy, availability and irreversibility

This topic relates to the maximum useful work that you can do with a system in a giventhe system moves to the state of the environment (called the dead state).

Profs. Lee and Bergthorson cover this material in a different way, so I wont go over it Go over this material if you dont remember how exergy is defined.

Calculation of exergy for complex engineering systems are done in industrial systems toptimize the efficiency of the system. We wont develop the concept of exergy further2.


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Thermo 1 review (or not), contd: Properties of Pure Substa

Background reading: Cengel & Boles (and Moran & Shapiro), Chap. 3

A pure substance has a fixed chemical composition. Which of the following are pure substances?

Phases of a pure substance:

Solid Liquid


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Compressed Liquid and Saturate

A saturated liquid is Also called a subcooled liquid, a liquidin this state in not about to vaporize

water


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Saturated Vapour, Saturated Vapour and Suand Sat. Liquid mixture

A vapour in equilibrium with a liquid is called a saturated vapour/liquid mixture. A saturatcondense. A superheated vapour is heated above the normal saturation temperature (temperaturevapour and liquid are in equilibrium) and hence is not about to condense.


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Saturation Temperature and Pressure

The saturation temperature is the temperature at which a pure substance changes phase. For water, at 1 atm, thtemperature is the same as the normal boiling point.

Temperature-Volume (T-v) diagram for the heatingprocess of water at a constant pressure of 1 atm


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Latent Heat

The energy absorbed or released during a phase change is called the latent heat, e.g., lafreezing) or latent heat of vaporization (for vaporization). A phase change from a solid to gas is casublimation.

During a vaporization process, the liquidand vapour are in equilibrium (at thesaturation p and T) and pressure andtemperature remain fixed. The relationbetween p and T during this phase changeis called the liquid-vapour saturationcurve:


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Property Diagrams: T-v diagram

Constant pressure lines on a T-v diagra

At supe(p > pphase-process


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T-v diagram, continued:

Note the shape of the constant pressure lines


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p-v diagram:

Note the shape of the constant temperature lines


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p-v diagram, including the freezing/melting curve (for water which expands upon freezing):

Note the triple line where the liquid, vapour and solid are all in equilibrium


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p-T diagram (often called the phase diagram):


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The p-v-T surface

Since the state of a simple compressible substance is fixed by 2 independent properties, p = p(v, T), for exampdefines a surface:

This substance contracts on freezing This substance expan


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For saturated liquid-vapour mixtures, the ratio of the mass of vapour to the total mass of the mixture is called quality,x :

x = m vapour /m total

In the 2-phase region, all properties can be written as a weighted sum of the saturated liquid and vapour value

V = V liq + V vap = m liqv f + m vapv g and now divide by mtotal: V/m = v

v avg = xv g + (1 x )v f = v f + x (v g v f ) = v f + xv fg

so x = (v avg v f )/v fg


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The energy functions can also be written as a sum in the saturation region, i.e.,

h = h f + x (h g h f ) = h f + xh fg,

where hfg is referred to as the enthalpy of vaporization.

Reference State and Reference Values

The values of the energy functions ( u, h, etc.) cannot be measured directly, only the changes in these we need to choose a reference state and assign a value of zero at that state. For water, the state of sat 0.01C is taken as the reference state.

Note that some tables choose a different reference point for u = 0 and h = 0 and so mixing prdifferent tables should be avoided.


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Approximations for liquids:

Specific volume and internal energy are not very sensitive to p, so the following approximations

engineering calculations:

So if compressed liquid tables are not available, the specific volume and

internal energy in the subcooled region can be estimated to a goodapproximation by using saturation values for a saturated liquid at thesame temperature.

v T,p vf T ; u T,p uf T

and since h u + pv, h T,p uf T + pvf T


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Incompressible Assumption:

To simplify evaluations involving liquids and solids, it is often assumed that the specific volume (or density)

constant and the specific internal energy is assumed to vary only with temperature. A substance idealized in tis called incompressible, i.e., in summary for an incompressible substance

1 = 1/v = constant and

(2) u = u (T ) only

In this case

Enthalpy varies with p and T:

So since v is constant for an incompressible substance,

cv = dudT

h T, p = u T + pv

cp =

hT p

= dudT

= cv


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Hence

And if c is taken as a constant, then for an incompressible substance

cv = cp = c

u = c Th = c T + v p


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Example 2:Water is contained in a piston-cylinder assembly at ( p, T) = (10 bar, 400

C).

Process 1-2: water cooled at constant pressure to saturation conditions.

Process 2-3: cool at constant volume to 150

C.

(a) Sketch processes on p-v, p-T and T-v diagrams.(b) Find work and heat transfer, per unit mass.


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Is Water Vapour an Ideal Gas?

Yes, but only for certain regions(relatively low pressures and away fromthe 2-phase region).

To the right is shown the % error in thespecific volume comparing the steamtables with the ideal gas assumption:


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Compressibility Factor,Z

The dimensionless ration pv/RT is called the compressibility factor,Z and it gives a measure of the divergence from ideal gas

behaviour.

When the compressibility factor is plotted versus reduced pressurefor a given reduced temperature, where

pR = p/pc and TR = T/Tc

also define a pseudo-reduced volume

c

cRpTR

vv

the results for most gases coincide (for 30 different gases, the deviation from the average is at most on the ord5% and for most ranges is much less). This is referred to as the principle of corresponding st

The chart produced is referred to as a generalized compressibility chart.


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Generalized Compressibil ity Chart


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Supplementary Reading: Heat and Work

Excerpt from Thermodynamics by Herbert Callen

It will be noted that we use the terms heat and heat flux interchangeably. Heat, like work, is onlya form of energy transfer . Once energy is transferred to a system, either as heat or as work, it isindistinguishable from energy which might have been transferred differently. Thus, although Q and

W add together to give dU , there are no quantities Q nor W which have any separate meanings. Theinfinitessimal quantity W is not a differential of some hypothetical function W , and to avoid thisimplication we use the symbol . This is true also of the quantity Q . Mathematically, infinitesimalssuch as W and Q are called imperfect differentials .

The concepts of heat, work, and energy may possibly be clarified in terms of a simple analogy.A certain gentleman owns a little pond, fed by one stream and drained by another. The pond alsoreceives water from an occasional rainfall and loses it by evaporation, which we shall consider asnegative rain. In the analogy we wish to pursue the pond is our system, the water within it is theinternal energy, water transferred by the streams is work, and water transferred as rain is heat.

The first thing to be noted is that no examination of the pond at any time can indicate how muchof the water within it came by way of the stream and how much came by way of rain. The term rainrefers only to a method of water transfer .

Let us suppose that the owner of the pond wishes to measure the amount of water in the pond.He can purchase flow meters to be inserted in the streams, and with these flow meters he can measurethe amount of stream water entering and leaving the pond. But he cannot purchase a rain meter.However, he can throw a tarpaulin over the pond, enclosing the pond in a wall impermeable to rain (anadiabatic wall). The pond owner consequently puts a vertical pole into the pond, covers the pond withhis tarpaulin, and inserts his flow meters into the streams. By damming one stream and then the other,

he varies the level in the pond at will, and by consulting his flow meters he is able to calibrate the pondlevel, as read on his vertical stick, with total water content ( U ). Thus, by carrying out processes on thesystem enclosed by an adiabatic wall, he is able to measure the total water content of any state of his

pond.Our obliging pond owner now removes his tarpaulin to permit rain as well as stream water to

enter and leave the pond. He is then asked to ascertain the amount of rain entering his pond during a particular day. He proceeds simply: he reads the difference in water content from his vertical stick, andfrom this he deducts the total flux of stream water, as registered by his flow meters. The difference is aquantitative measure of the rain. The strict analogy of each of these procedures with the thermodynamiccounterparts is evident.

Since work and heat refer to particular modes of energy transfer, each is measure in energy units.

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