THERMODYNAMICS 1. Volumetric Properties of Pure Fluids. Department of Chemical Engineering, Semarang State University Dhoni Hartanto S.T., M.T., M.Sc.

Size: px

Start display at page:

Download "THERMODYNAMICS 1. Volumetric Properties of Pure Fluids. Department of Chemical Engineering, Semarang State University Dhoni Hartanto S.T., M.T., M.Sc."

Branden Flowers
6 years ago
Views:

1 ompany LOGO THERMODYNAMIS olumetric roperties of ure Fluids Department of hemical Engineering, Semarang State University Dhoni Hartanto S.T., M.T., M.Sc.

2 Introduction ressure, olume, and Temperature (T) are important properties such purposes as the metering of fluids and the sizing of vessel and pipelines. Quantitive description of real fluids Equation of State (EoS) Generalized correlation are used to predict T behaviour of fluid which has no experimental data

3 T ehaviour of ure Substances T Diagram : critical point (critical pressure c and T c ) the highest temperature and pressure at which a pure chemical species can exist in vapor/liquid equilibrium c Solid 3 Liquid A Fluid In critical condition, fluid is classified as liquid or gas (the two phase become indistinguishable) Triple point apor Gas Region Gas in left side of dashed line can be condensed as vapor Sublimation curve T T c Gas in right side of dashed line (T >T ) is supercritical condition

4 Solid Solid+Liquid Liquid T ehaviour of ure Substances Diagram to line single-phase saturated liquids at their boling temperature to D line single-phase saturated vapor at their condensation temperature c Fluid Under curve D : Subcooled-liquid (T below T boiling) Superheated-vapor (T above T boil.) Liquid+apor Solid+apor T<T c D T c T>T c L c

5 T ehaviour of ure Substances Equation of State (EoS) : Functional equation to express the relation between,, and T f (,, T) 0 artial derivatifve : d T dt T d artial derivatifve related to properties: olume expansivity : Isothermal compressibility: T T Thus: d dt d

6 ln T ehaviour of ure Substances If and are constant (for liquid approximation) T T Simple EoS Is almost always positive, is necessarily positive The value of dan has been commonly tabulated T relation

7 T ehaviour of ure Substances Example : Acetone at 93.5 K and bar has =.487 x 0-3 K -, = 6 x 0-6 bar -, and =.87 x 0-3 m 3 kg - a) Find the value of ( / T ) b) The pressure generated when acetone is heated at constant volume from 93.5 K and bar to K c) The volume change when acetone is changed from 93.5 K and bar to 73.5 K and 0 bar Solution : a) d dt d is constant d = 0, 0 dt d T bar K 6 6 0

8 T ehaviour of ure Substances Solution : b) The value of and can be assumed constant at interval temperature 0 K The equation in (a) : T ( 4)(0) 40bar and 40 4bar c) ln T T 3 ln (.4870 ) 6 0 (60 ) ; 0.970(.870 (.49.87)(0 3 3 ).490 ) (0.038)(0 3 ) m 3 3 m kg 3 kg

9 irial Equation of State Equation of State (EoS) f (,, T) 0 Gas Ideal (Simplest EoS) - olume individual = 0 - No interaction - alid in low pressure Real Gas ; ompressibility factor () For ideal gas, =

10 T ehaviour of ure Substances irial EoS D D... irial expansions, : -body interaction and 3-body interaction between pairs of molecules ' and ' and : : Second virial coefficients Third virial coefficients For a given gas the virial coefficients are functions of temperature only ' ; ' ( ) ; D' D 3 3 ( ) 3

11 T ehaviour of ure Substances Truncated irial EoS The value has been tabulated for various gases Application : a) Gas phase only (satisfactory results for vapor at subcritical T) b) Significantly molecul interactions c) For low pressure gas (up to a pressure about 5 bar)

12 Application of the irial Equation Originate value at = for = 0 The tangent to an isotherm at = 0 is good approximation T; Tangent line eq. :

13 Application of the irial Equation The pressure above the range eq. in previous slide but below critical pressure three term virial equation give excellent result alue of and depend on the gas and on temperature In figure 3., the trends are similar

14 Application of the irial Equation Ideal gas Equation of State irial EoS If: D 3 0 or... or Assumption : no molecule interaction Good approximation for gas : in very low pressure or high temperature (big olume)

15 Application of the irial Equation Internal energy for ideal gas U U T, for real gas depend on molecule interaction In ideal gas, no molecule interaction occured (= infinite) U UT Enthalpy for ideal gas H U H U H H(T )

16 Application of the irial Equation Heat capacity for ideal gas U T U UT (T ) H T H HT (T ) The relation between and for ideal gas dh du d( ) p R p dt dt RdT

17 Application of the irial Equation Extended virial equation (enedict/webb/rubin Equation) A / T b a a exp 6 3 c T Where : A0, 0, 0, a, b, c,, are all constant for a given fluid This complex equation are used in the petrolium and natural-gas industries (light hydrocarbon and a few gas)

18 Application of the irial Equation Example The virial coefficients of isopropanol vapor at 00 o : = -388 cm 3 mol - ; = cm 6 mol - alculate and for isopropanol vapor at 00 o and 0 bar by using : a) The ideal-gas equation b) Eq.3.37 (Smith an Ness Handbook 6 th ed) c) Eq.3.39 (Smith an Ness Handbook 6 th ed) Solution : The absolute temperature is T = K, gas constant (R) = 83.4 cm 3 bar mol - K - a) Ideal gas, = (83.4)(473.5) 3934 cm 3 mol - 0

19 Application of the irial Equation b) Solving eq for : 3934 ( 388) 3546 cm 3 mol - / c) Solving eq. 3.39, rearrange equation to facilitate iteration, yield : i i i Using goal seek in M. Excel to obtain, then = 3488 cm 3 mol - / The ideal gas value is 3% too high and no (b) is.7% too high compare with this result

Chapter 3 PROPERTIES OF PURE SUBSTANCES. Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008

Chapter 3 PROPERTIES OF PURE SUBSTANCES Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 Objectives Introduce the concept of a pure substance. Discuss