Macroscopic Description of Thermodynamic Systems

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Virtual, Practicable, Economic & Useful Means…

Why Description of System ???

Microscopic Description may be Real …Still Humans Believe in Macroscopic Description ..

• Macroscopic Ohm’s law: The resistance R of a conductor is the ratio of the potential difference V between the two ends of the conductor and the current I:

I

VR

Resistance is related to resistivity by

A

lR

Microscopic Truth

Macroscopic Description• Whatever felt by human sense(About any thing) is the truth,

with/without much help of detailed training.

Macroscopic Description of A System

• This Description is based on all those effects, that are perceived by human senses.

• Gross or average effects of many molecules are described and measured.

• This description is the time-averaged influence of many molecules.

• Instruments are to be designed to quantify these effects.

• Engineering Thermodynamics uses Macroscopic Description.

A Virtual Description of a System but truly practical.

The Foremost Macroscopic Description Parameter

Fundamental Characteristics used in Macroscopic Description

• LENGTH (m)– AREA (sq. m)

– VOLUME (cu. m)

• TIME (s, min, h)– VELOCITY (m/s)

– ACCELERATION (m/s2)

• MASS (kg)– FORCE or WEIGHT (N)

– PRESSURE (kPa, mm of Hg, m of water)

Thermodynamic Property

• Any suitable characteristic whose value depends on the condition of a system and which is relevant to our thermodynamic study is known as a Thermodynamic Property.

• When nothing happens to this system , each of the properties of a system (substance) has only one definite value.

• These properties always have the same value for a given condition, regardless of how the substance arrived at the condition.

Robert Boyle

•17th-century natural philosopher, chemist, physicist, and inventor, also noted for his writings in theology.• Scientific interest in the manufacturing of gas produced by the natural decomposition of organic matter, was first reported in the seventeenth century by Robert Boyle

Unlike most scientists of the day, Boyle did not seek to discover new things by arguing matters logically. Instead he was interested in making observations and drawing conclusions based on these. It was Boyle who started the practice of conducting controlled experiments. He used to publish his experiments while noting down his practices and the various apparatus that he used. 

Classification of Properties

• Based on method of Measurement:

– Primitive Property -- Directly observable -- With simple experiments -- No change in system.

– Derived Property -- Vigorous experiments -- To be calculated using observations.

• Computational basis:

– Intensive property -- Local property -- Independent of mass or size of the system.

– Extensive property -- depends on the extent of the system.

Van der Waals EOS

• One of the oldest but most extensively used of the EOS of non-ideal gases

• Any EOS model must reproduce graphs such as that of the previous

R

T

bv

v

ap

2

•a & b are the Van der Waals constants for the particular gas;

•for N2: a = 0.14 J-m3/mole2; b = 3.9x10-5 m3/mole,

The constants a, b, c & R varies with substance

Beattie-Bridgeman Equation

R

vb

BvvT

cT

va

Apv

11

1

03

02

How to Get An Objective Method to Identify more Properties…..

Created A New Branch in Mathematics !!!

The Functional Relation for Description

• What kind of Functional Relation?

• Assume that variables p, V, T are functionally related.

• Say F(p, V, T) = Constant.

• Assume that each variable can be explicitly “solved” from this functional relation in terms of two other variables, which are allowed to vary freely.

• p to obtain an expression of the form p = g(V, T), where V and T are chosen as free variables.

• Any function of p, V, T can be expressed as a function of any pair of free variables of your choice.

• F(p, V, T) = F(g(V, T), V, T) is expressed as a function of a pair of free variables V and T.

Functions of Several Variables

• Develop a function using these variables : F(x,y,z,…)

• If F(x,y,z,……) = Constant.

• This is called as Pfaffian function.

• Pfaffian function is denoted as F(.) and called as Point Function.

A total change in point function is expressed as:

0,,,

dzz

Fdy

y

Fdx

x

FdF

yxxzzy

Define functions M,N & P such that:

dzzyxPdyzyxNdxzyxMdF ),,(),,(),,(

As F(x,y,z) is a point function, differentiation is independent of order.

zyzxx

N

y

M

,,

This is called as pfaffian differential equation.

Properties of A Point Function

zxyx y

P

z

N

,,

yxzy z

P

x

P

,,

vp p

K

v

I

The necessary and sufficient condition for g to be accepted as a property is.

Creation of New Variable in Thermodynamics

dvvpKdpvpIdg ),(),(

If we develop an equation for change in a new characteristic of any thermodynamic system as

The variable g can provide a functional relationship

0),,(),,(),,( dggvpLdvgvpKdpgvpIdj

vpgvgvvpgvgp g

I

p

L

p

L

g

K

p

K

v

I

,,,,,,

;;

j(p,v,g)= Constant

Definition of A Thermodynamic Property

• Any Macroscopic variable, which can be written as a point function can be used as a thermodynamic property

• Thermodynamic properties are so related that F(.) is constant.

• Every substance is represented as F(.) in Mathematical (Caratheodory) Thermodynamics.

• This is shows a surface connectivity of Property of a substance.

p-v-T Diagram of solid Phase

Top View : V – T Diagram

Front View : p – V Diagram

Volume

Temperature

Pressure