Chapter 4: Properties of Pure Substances. Pure Substance. Phases of a Pure Substance. Phase-Change Processes of Pure Substances

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1 Chapter 4: roperties o ure Substances ure Substance A substance that has a ixed chemical composition throughout is called a pure substance such as water, air, and nitrogen A pure substance does not hae to be o a single element or compound A mixture o two or more phases o a pure substance is still a pure substance as long as the chemical composition o all phases is the same hases o a ure Substance A pure substance may exist in dierent phases here are three principle phases solid, liquid, and gas A phase: is deined as haing a distinct molecular arrangement that is homogenous throughout and separated rom others (i any) by easily identiiable boundary suraces A substance may hae seeral phases within a principal phase, each with a dierent molecular structure For example, carbon may exist in as graphite or diamond in the solid phase, and ice may exist in seen dierent phases at high pressure Molecular bonds are the strongest in solids and the weakest in gases Solid: the molecules are arranged in a three-dimensional pattern (lattice) throughout the solid he molecules cannot moe relatie to each other; howeer, they continually oscillate about their equilibrium position Liquid: the molecular spacing in liquid phase is not much dierent rom that o the solid phase (generally slightly higher), except the molecules are no longer at ixed positions relatie to each other Gas: the molecules are ar apart rom each other, and a molecular order does not exist Gas molecules moe randomly, and continually collide each other and the walls o the container they are in Molecules in the gas phase are at a considerably higher energy leel than they are in liquids or solid phases hase-change rocesses o ure Substances Consider a process that a pure substance starts as solid and is heated up at constant pressure until it all becomes as gas Depending on the preailing pressure, the matter will pass through arious phase transormations At 0: 1 Solid Mixed phase o liquid and solid Chapter 4, SYDE 81, Spring 014 1

2 Sub-cooled or compressed liquid (means it is not about to aporize) 4 Wet apor or saturated liquid-apor mixture, the temperature will stop rising until the liquid is completely aporized 5 Superheated apor (a apor that is not about to condense) Chapter 4, SYDE 81, Spring 014 Fig 4-1: -V diagram or the heating process o a pure substance At a gien pressure, the temperature at which a pure substance starts boiling is called the saturation temperature, sat Likewise, at a gien temperature, the pressure at which a pure substance starts boiling is called the saturation pressure, sat During a phase-change process, pressure and temperature are dependent properties, sat = ( sat )

3 he critical point is the point at which the liquid and apor phases are not distinguishable he triple point is the point at which the liquid, solid, and apor phases can exist together On - or - diagrams, these triple-phases states orm a line called the triple line able 4-1: Critical and triple point or water and oxygen Critical oint riple oint (atm) (K / C) (atm) (K / C) H O /(7414) (001) O /( 1186) /( 19) Vapor Dome he general shape o a - diagram or a pure substance is ery similar to that o a - diagram critical point sat apor line SUERHEAED VAOR REGION COMRESSED LIQUID REGION sat liquid line SAURAED LIQUID-VAOR REGION = const > 1 1 = const Chapter 4, SYDE 81, Spring 014 Fig 4-: - diagram o a pure substance he - or hase Change Diagram his is called phase diagram since all three phases are separated rom each other by three lines Most pure substances exhibit the same behaior One exception is water Water expands upon reezing

4 Fig 4-: phase diagram o pure substances here are two ways that a substance can pass rom solid phase to apor phase i) it melts irst into a liquid and subsequently eaporates, ii) it eaporates directly without melting (sublimation) the sublimation line separates the solid and the apor the aporization line separates the liquid and apor regions the melting or usion line separates the solid and liquid these three lines meet at the triple point i <, the solid phase can change directly to a apor phase at < the pure substance cannot exist in the liquid phase Normally (> ) the substance melts into a liquid and then eaporates matter (like CO ) which has a triple point aboe 1 atm sublimate under atmospheric conditions (dry ice) or water (as the most common working luid) we are mainly interested in the liquid and apor regions Hence, we are mostly interested in boiling and condensation Chapter 4, SYDE 81, Spring 014 4

5 roperty ables For most substances, the relationships among thermodynamic properties are too complex to be expressed by simple equations hus, properties are requently presented in the orm o tables, see able A-4 he subscript is used to denote properties o a saturated liquid and g or saturated apor Another subscript, g, denotes the dierence between the saturated apor and saturated liquid alues o the same property For example: = speciic olume o saturated liquid g = speciic olume o saturated apor g = dierence between g and ( g = g ) Enthalpy: is a property deined as H = U + V (kj) or h = u + (kj/kg) (per mass unit) Enthalpy o aporization (or latent heat): represents the amount o energy needed to aporize a unit mass o saturated liquid at a gien temperature or pressure It decreases as the temperature or pressure increase, and becomes zero at the critical point 1- Saturated Liquid-Vapor Mixture During aporization, a mixture o part liquid part apor exists o analyze this mixture, we need to know the proportions o the liquid and apor in the mixture he ratio o the mass o apor to the mass o the total mixture is called quality, x: m apor x = mtotal = mliquid + mapor = m + m g m total Saturated liquid-apor mixture is treated as a combination o two sub-systems (two phases) he properties o the mixture are the aerage properties o the saturated liquid-apor mixture V = V + Vg mtae = m + mgg m = mt mg mtae = ( mt mg ) + mgg diiding by m t = 1 x + x and x = m / m ae ( ) ae = + x or, ae x = g g g ( m / kg) g t Chapter 4, SYDE 81, Spring 014 5

6 or critical point sat liquid states sat apor states sat apor sat liquid Fig 4-4: he relatie amounts o liquid and apor phases (quality x) are used to calculated the mixture properties Similarly, u h ae ae = u = h + xu + xh Or in general, it can be summarized as y ae = y +xy g Note that: 0 x 1 y y Remember: pressure and temperature are dependent in saturated mixture region ae y g g g Fig 45: Quality deines only or saturated liquid-apor mixture Chapter 4, SYDE 81, Spring 014 6

7 Example 4-1: Saturated liquid-apor mixture A closed, rigid container o olume 05 m is placed on a hot plate Initially the container holds a two-phase mixture o saturated liquid water and saturated water apor at 1 = 1 bar with a quality o 05 Ater heating, the pressure in the container is =15 bar Indicate the initial and inal states on a - diagram, and determine: a) the temperature, in C, at each state b) the mass o apor present at each state, in kg c) i heating continues, determine the pressure, in bar, when the container holds only saturated apor Solution: Assumptions: 1 Water in the container is a closed system States 1,, and are equilibrium states he olume o container remains constant wo independent properties are required to ix state 1 and At the initial state, the pressure and quality are known hus state 1 is known, as shown in the igure he speciic olume at state 1 is ound using the gien quality: 1 = 1 + x1 ( g1 1 ) From able A - 5 at = 1bar = ( ) = m / kg 1 At state, the pressure is known Volume and mass remain constant during the heating process within the container, so = 1 For = 15, able A-5 gies = and g =1159 m /kg Since < < g State must be in the two-phase region as well Since state 1 and are in the two-phase liquid-apor region, the temperatures correspond to the saturation temperatures or the gien able A-5: 1 = 996 C and = 1114 C o ind the mass o water apor present, we irst ind the total mass, m V 05m m = = = 059kg 08475m / kg mg1 = x1m = ( 059kg) = 0 kg Chapter 4, SYDE 81, Spring 014 7

8 = 15 bar 1 = 1 bar 1 he mass o apor at state is ound similarly using quality x From able A-5, or = 15 bar, we hae: Chapter 4, SYDE 81, Spring 014 x x m = g g = = = 071 ( 059kg) = 041 kg I heating continued, state would be on the saturated apor line, as shown in on the - diagram aboe hus, the pressure would be the corresponding saturation pressure Interpolating in able A-5 at g = m /kg, we get = 11 bar - Superheated Vapor Superheated region is a single phase region (apor only), temperature and pressure are no longer dependent See able A-6 or superheated apor properties I >> critical or << critical, then the apor can be approximated as an ideal gas - Compressed (or Sub-cooled) Liquid he properties liquid are relatiely independent o pressure (incompressible) A general approximation is to treat compressed liquid as saturated liquid at the gien temperature y 8

9 he property most aected by pressure is enthalpy For enthalpy use the ollowing approximation: h he Ideal-Gas Equation o State + ( ) Any equation that relates the pressure, temperature, and speciic olume o a substance is called an equation o state he simplest and best known equation o state or substances in the gas phase is the ideal-gas equation o state Gas and apor are oten used as synonymous words he apor phase o a substance is called a gas when it is aboe the critical temperature Vapor usually implies a gas that is not ar rom a state o condensation It is experimentally obsered that at a low pressure the olume o a gas is proportional to its temperature: = R Where R is the gas constant he aboe equation is called the ideal-gas equation o state (ideal gas relation) Since R is a constant, one can write: 1 1 R = = 1 he constant R is dierent or each gas; see able A-1 in Cengel book R u = 814 kj / (kmol K) is the uniersal gas constant, R = R u /M he Molar mass, M: is deined as the mass o one mole o a substance (in gmole or kgmol) he mass o a system is equal to the product o its molar mass M and the mole number N: sat m = MN (kg) See able A-1 or R and M or seeral substances An ideal gas is an imaginary substance that obeys the relation = R It is experimentally obsered that the ideal gas closely approximate the -- behaior o real gases at low densities in the range o practical interest, many amiliar gases such as air, nitrogen, oxygen, hydrogen, helium, argon, neon, and CO can be treated as ideal gases with negligible error water apor (in general see Fig 4-49 Cengel book), rerigerant apor in rerigerators should not be treated as ideal gases water apor at pressures below 10 ka can be treated as an ideal gas, regardless o temperature Chapter 1, SYDE 81, Spring 014 9

10 Compressibility Factor he assumption o ideal gas relation implies that: the gas particles take up negligible olume the intermolecular potential energy between particles is small particles act independent o one another Howeer, real gases deiate rom ideal gas behaior his deiation at gien temperature and pressure can be accurately accounted or by introduction o a correction actor called the compressibility actor Z Z = or = ZR R or Z = actual / ideal Obiously, Z=1 or ideal gases Gases behae ery much the same at temperatures and pressures normalized with respect to their critical temperatures and pressures R = and R = cr Here R and R are called the reduced pressure and temperature, respectiely By cure-itting all the data, the general compressibility chart is obtained which can be used or all gases cr Fig 4-6: Z actor, general compressibility chart Chapter 4, SYDE 81, Spring

11 From the Z chart, one can conclude: at ery low pressure ( R <<1), the gases behae as an ideal gas regardless o temperature at high temperatures ( R >), ideal gas behaior can be assumed the deiation is highest in the icinity o the critical point Example 4-: Ideal Gas Determine the speciic olume o R-14a at 1 Ma and 50 C, using (a) ideal gas equation (b) the generalized compressibility chart Compare the alues obtained with the actual alue o m /kg Solution: From able A-1, or R-14a, R = kam /(kgk), cr = 4067 Ma, and cr = 74 K (a) Ideal gas equation o state [ 0815 ka m /( kg K )]( K ) ( 1000 ka) 0 R = = = 006 m / kg Comparing with the tabulated alue, using ideal gas equation one would get an error o ( )/00171=01 or 1% (b) o determine the correction actor Z, R R = cr = cr 1Ma = = Ma K = = K From Fig 4-51, Z= 084 hus, =Z ideal = 084 (006 m /kg) =0011 m /kg he error is less than % hereore, in the absence o exact tabulated data, the generalized compressibility chart can be used with conidence Chapter 4, SYDE 81, Spring