thermodynamics 1 - properties of pure substances

Chapter 3 Thermodynamics 1 1

Thermodynamics I

Introduction 1. Basic Concepts of Thermodynamics 2. Energy, Energy Transfer, and General Energy Analysis 3. Properties of Pure Substances 4. Energy Analysis of Closed Systems 5. Energy and Mass Analysis of Control Volumes 6. The Second Law of Thermodynamics 7. Entropy 8. Steam Power Cycle Applications Examples

Chapter 3 EG-161: Thermodynamics 1 2

Overview Properties of Pure Substances

3-1 Pure Substance 3-2 Phases of a Pure Substance 3-3 Phase-Change Processes of Pure Substances 3-4 Property Diagrams for Phase-Change Processes 3-5 Property Tables 3-6 The Ideal-Gas Equation of State 3-7 Compressibility Factor


Pure Substance A pure substance has a

fixed chemical composition throughout various processes.

Examples are: water, nitrogen, helium and carbon dioxide.

Homogeneous mixtures also qualify as pure substances (e.g. air).

A mixture of two or more phases can still be a pure substance.


Phases of a Pure Substance 3 principal phases: solid, liquid and

gas-phase. Substances may have several phases

with the principal phase (e.g. ice has 7, iron has 3, carbon has 2).


Phase-Change Processes

Subcooled/compressed liquid

Saturated Liquid Saturated Liquid-Vapour Mixture

Saturated Vapour

Superheated Vapour


Property Diagrams for Phase-Change Processes: T-v


Property Diagrams for Phase-Change Processes: P-v


Rankine Cycle - Phase Change


Saturation Temperature and Saturation Pressure

The temperature at which water starts boiling depends on the pressure.

If the pressure is fixed, so is the boiling temperature. During the phase change the two phases are in equilibrium. For a pure substance and a given pressure the phase-change

temperature is called saturation temperature Tsat. For a pure substance and a given temperature the phase-change

pressure is called saturation pressure Psat.


Some Consequences of Tsat and Psat Dependence

The temperature of liquid nitrogen exposed to the atmosphere remains constant at 196C, and thus it maintains the test chamber at 196C.

In 1775, ice was made by evacuating

the air space in a water tank.


P-v Diagram for Substance that Contracts/Expands on Freezing


P-T or Phase Diagram

Substance Ttp (K) Ptp (kPa) Water 273.16 0.61

Nitrogen 63.18 12.6

Latent heat of sublimation/ deposition

Latent heat of vaporization/ condensation

Latent heat of fusion


Enthalpy

Enthalpy is a combination property. In the analysis of cycles we

frequently encounter the expression:

U+PV For simplicity reason this quantity

is termed enthalpy: H=U+PV (kJ) h=u+Pv (kJ/kg)


Saturated Liquid and Vapour States

vf: specific volume of saturated liquid

vf vg vg: specific volume of saturated vapour

fg g f

fg g f

fg g f

fg g f

v v vu u uh h hs s s

=

=

=

=


A rigid tank contains 50 kg of saturated liquid water at 90C. Determine the pressure in the tank and the volume of the tank.

Saturated Liquid and Vapour States Example

Answer: P=70.18kPa V=0.0518m3


A mass of 200g of saturated liquid water is completely vaporized at a constant pressure of 100kPa. Determine a) the volume change and b) the amount of energy added to the water.

Saturated Liquid and Vapour States Example

Answer: DV=0.3386m3 DE=451.6kJ


To analyse a liquid-vapour mixture in the wet-region we need to know the proportions of the liquid and the vapour phases.

The new property is called quality x:

where

Saturated Liquid-Vapour Mixtures Quality x

1

vapour

total

liquid

total

mx

mm

xm

=

=

: mass fraction of vapour

: mass fraction of liquid (or simply moisture)

total liquid vapour f gm m m m m= + = +

(

using 1

or1 )

f g

f g gf f g

f g f fg

g

V V Vm m m m

mv m v m v x xm m m

v x v xv v v xv

= +

= + = =

= + =

=

+

and


Saturated Liquid-Vapour Mixtures Quality x

f

fg

f fg

f fg

f fg

f fg

v vx

vv v xv

u u xuh h xhs s xs

=

= +

= +

= +

= +


Saturated Liquid-Vapour Mixtures Example

Answer: P=70.18kPa V=4.73m3

A rigid tank contains 10 kg of saturated liquid water at 90C. If 8 kg of the water is in the liquid phase and the rest is in the vapour phase, determine a) the pressure in the tank, and b) the volume of the tank.


Saturated Liquid-Vapour Mixtures Example

Answer: T=Tsat@kPa=-15.60C x=0.158 h=62.7kJ/kg mg=0.632kg and Vg=0.0777m3

An 80 L vessel contains 4 kg of refrigerant 134-a at a pressure of 160kPa. Determine a) the temperature of refrigerant, b) the quality, c) the enthalpy of the refrigerant, and d) the volume occupied by the vapour phase.

1


Compressed Liquid A compressed liquid is to be approximated as saturated liquid at

the given temperature. The properties depend more on the temperature than they do

on the pressure.

Example: Determine the internal energy of compressed liquid water at 80C and 5 MPa: From compressed liquid table:

u=333.72kJ/kg From saturation table:

u334.86kJ/kg Error: 0.34%


Superheated Vapour Pressure and

Temperature are no longer dependent variables.

Super-heated vapour is a single-phase substance.


Determine the temperature of water at a state of P=0.5MPa

and h=2890kJ/kg.

Answer:

At 0.5MPa saturated vapour: hg=2748.7kJ/kg. Therefore we have superheated vapour. Linear interpolation from tables gives: T=216.4C

Superheated Vapour Example


THE IDEAL-GAS EQUATION OF STATE

Equation of state: Any equation that relates the pressure, temperature, and specific volume of a substance.

The simplest and best-known equation of state for substances in the gas phase is the ideal-gas equation of state. This equation predicts the P-v-T behavior of a gas quite accurately within some properly selected region.

R: gas constant M: molar mass (kg/kmol) Ru: universal gas constant

Ideal gas equation of state P: absolute pressure T: absolute temperature in Kelvin


THE IDEAL-GAS EQUATION OF STATE

Different substances have different gas constants.

Various expressions of ideal gas equation

Ideal gas equation at two states for a fixed mass


Compressibility Factor The compressibility factor Z is a correction factor and is a

measure of the deviation from ideal-gas behaviour. Z is defined as:

ideal

actual

vvZ

ZRTPvRTPvZ

=

=

=

or

Thermodynamics IOverview Properties of Pure SubstancesPure SubstancePhases of a Pure SubstancePhase-Change ProcessesProperty Diagrams for Phase-Change Processes: T-vProperty Diagrams for Phase-Change Processes: P-vRankine Cycle - Phase Change Saturation Temperature and Saturation PressureSome Consequences of Tsat and Psat DependenceP-v Diagram for Substance that Contracts/Expands on FreezingP-T or Phase DiagramEnthalpySaturated Liquid and Vapour StatesSaturated Liquid and Vapour StatesExampleSaturated Liquid and Vapour StatesExampleSaturated Liquid-Vapour MixturesQuality xSaturated Liquid-Vapour MixturesQuality xSaturated Liquid-Vapour MixturesExampleSaturated Liquid-Vapour MixturesExampleCompressed LiquidSuperheated VapourSuperheated VapourExampleTHE IDEAL-GAS EQUATION OF STATETHE IDEAL-GAS EQUATION OF STATECompressibility Factor

thermodynamics 1 - properties of pure substances

Documents

law of thermodynamics

phasechange temperature

phasechange pressure

freezing chapter

phase diagram substance

u pv kjkg chapter

temperature of liquid

compressibility factor