P-T Diagram and Properties of Pure Substances: A Comprehensive Guide, Slides of Thermodynamics

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ENGI 2102 Thermo-Fluid Engineering I

Chapter 4: Thermodynamic Properties of Fluids

G. Mazzanti Process Engineering and Applied Science Dalhousie University Fall 2019 Slides by Michele Hastie, 2016

Outline

 4.1 The P - v - T Surface

 4.1.1. The P - v Diagram

 4.1.2. The T - v Diagram

 4.1.3. The P - T Diagram

 4.2 Property Tables and Charts

 4.3 The Ideal Gas Equation of State

 4.4 Methods for Nonideal Gases

 4.4.1 Cubic Equations of State

 4.4.2 Generalized Compressibility Charts

4.1 The P - v - T Surface (page 69)

https://www.patana.ac.th/secondary/science/anrophysics/unit5/commentary.htm Increasing temperature Increasing pressure Increasing volume, v [m 3 /kg] or V [m 3 ]

4.1 The P - v - T Surface (page 70)

 Suppose that heat is added to a substance at constant pressure:

T ν T ν A B C D E F A B C D E F liquid-solid solid-vapour solid liquid liquid- vapour vapour critical point constant P a) b)

Heat

Solid

a)

Liquid Heat b)

Liquid

Vapour

Heat

c)

Vapour

Heat

d)

T ν T ν A B C D E F A B C D E F liquid-solid solid-vapour solid liquid liquid- vapour vapour critical point constant P a) b)

4.1 The P - v - T Surface (page 72)

Fig. 4.3: P-v-T surface of a substance that contracts on freezing Triple line L-V Solid S-V S-L Liquid Vapour Gas Critical point constant P T = (^) T c

P

v

T

T ν A B C D E F liquid-solid solid-vapour solid liquid liquid- vapour vapour critical point constant P

4.1.1. The P - v Diagram (page 72)

Fig. 4.4: The P - v diagram for a pure substance

4.1.2. The T - v Diagram (page 74)

Fig. 4.6: The T - v diagram for a pure substance

 A vapour that cannot be condensed simply by increasing the pressure without changing the temperature is normally referred to as a gas.  Above the critical point , gas and liquid phases are indistinguishable and the fluid is called a supercritical fluid.

4.1.3. The P - T Diagram (page 74)

Fig. 4.7: The P - T diagram for a pure substance

 For a given pressure, liquid and vapour may exist in equilibrium at

any state ( T , v ) between the saturated points L and V.

 The total volume of the mixture in the liquid–vapour region is the

sum of the volumes occupied by the liquid and the vapour.

4.2 Property Tables and Charts (page 75)

Fig. 4.9: T - v diagram showing saturated liquid and vapour points

(4.3b)

4.2 Property Tables and Charts (page 77)

 The total volume (m 3 ) of the liquid-vapour mixture is,

or,

where m is mass (kg) and v is specific volume (m

3

/kg)

 The quality of the mixture is defined as the ratio of the mass of the saturated vapour to the total mass:  Quality can be expressed as a fraction (between 0 and 1) or a percentage (between 0 and 100%). V = VL + VV mv = mL vL + mVvV m m x V = (4.3a) (4.4) x = 0 (all saturated liquid) x = 0.5 (50% sat. liquid, 50% sat. vapour by mass) x = 1 (all saturated vapour)

4.2 Property Tables and Charts (page 78)

 Data is also often presented in graphical format.

 One example is the pressure vs. enthalpy ( P - h ) diagram.

P h critical point Lines of constant specific volume Lines of constant temperature Lines of constant dryness fraction Fig. 4.10: Pressure-enthalpy ( P - h ) diagram

4.2 Property Tables and Charts (page 78)

https://www.ohio.edu/mechanical/thermo/property_tables/H2O/ph_water.html

Gibbs Phase Rule

 The state of a system is described by giving values to its

properties (temperature, pressure, volume, etc .) at a

particular instant.

 The number of independent variables that must be

specified to fix the state of the system is given by the

Gibbs phase rule. The phase rule is:

# of variables = 2 – Π + N

 where:

 Π is the number of phases

 N is the number of chemical species

(3.2)

Gibbs Phase Rule

 In this course, we will only

consider systems involving

pure substances ( N = 1).

 For example, water can

exist as:

 Only intensive variables can be used to specify the state of a system:

 P , T , v , û , h , or s

 Extensive variables cannot be used ( e.g. , mass or volume). Number of phases # of variables Compressed liquid 1 2 – 1 + 1 = 2 Saturated liquid-vapour mixture 2 2 – 2 + 1 = 1 Superheated vapour 1 2 – 1 + 1 = 2