Thermodynamics Properties of pure fluids

Classification of TD properties:-

TD properties of fluids can be classified into 3 broad groups:

·        The reference props

·        Energy props and

·        The derived props

Reference Properties:-   Also known as primary props, that are used to define the state of the system. They have absolute values, which are measured relative to some arbitray reference state.

Ex:- Temperature, Pressure, Volume  and Entropy.

Where Tempr and Pressur are intensive and Volume and Entropy are Extensive props.

In solution the composition is also treated as a reference property.

Energy Properties:- The four energy props are internal energy (u), Enthalpy (H), the  Helmholtz  free energy (A), and Gibbs free energy (G) and all are extensive TD props and known as relative to some ref. State.

These are referred as energy props, because the changes in the these TD function indicate useful work under certain condition of restraint.

Derived properties:- These are partial derivatives of energy props or the reference props.

EX:- Specific height (C) , co-efficient of expansion ( β) , Joule –Thomson coeff(μ) & Co-efficient of compressibility ( K).

Work Function:- (HELMHOLTZ FREE ENERGY)

The Helmholtz free energy (A) of a system is defined as A=U-TS where U, T & S are the I.E , Temperature and Entropy of the system resp.

A is an extensive property , Since U & S are both extensive & it is also a state function.

Thermodynamics properties or Fundamentals Property rules:-

WKT  First Law for Closed System is ΔU=Q-W  =>  du =dq-dw  .

By Defination dq = ds / T  => dq = TdS and also dw=pdv

There fore  du=TdS – pdv  ------------------------- (1)

First law for open System :- ΔH-q- ws , dh= dq-dws

By defn. dq = TdS , dws = -vdp

There fore dH=TdS+ vdp----------------------------(2)

Some Definition and Terminologies:-

Helmholtz free energy or work function (A):_

A = u –TS---------------------------( 3)

dA= du- TdS  - SdT   => dA = TdS   - pdv – sdT – Tds

Substitute du from Eqn. (1).

dA= -pdv – sdT----------------( 4 )

Gibbs free energy (G) or (F):-    G=H – TS------------------( 5)

dG = dH – TdS – Sdt

Substitute for dH ,    dG= vdp – SdT-----------------( 6)

Eqn. (1) (2)(4)& (6) are known as fundamental property relations.

If at every instant, the external electric system is made to exert such a large counter emf, that when infinitesimally fused, then current will be forced in the opposite direction , thus reversing the reaction.

The decrease in the work function in the process would be equal to the total work done by the system. Which include both the electrical work & the work  of expansion.

A is a state for j – ΔA would be the same for reverse as well as for irreversible process occurring between the same end states.

In the above processes, the decrease in Helmholtz free energy determines the max. work  which includes the electrical energy & the work of expansion resulting from the reaction.

WR= - ΔA  ,  WR’ = -ΔG

The change in Gibbs free energy G measure the net useful work, it is known as the “Free Energy”.

The Value of ΔG in any process is quite definite, no matter under what condition the process is carried out , but only when T & P are const the free energy change would represent the max. net work available  from the given change in state.

Property Relation

du= Tds – Pdv

dH= Tds + vdp

dA= -pdv-SdT

dG= vpd - SdT

FUGACITY (f):- The concept of fugacity was introduced by G.N Lewis (1901) & is widely used in solution TD to represent the behaviour of real gases. The name fugacity is derived from the Latin for ‘fleetness’ or the ‘Escaping tendency’. It has been used extensively in the study of phase & chemical reaction equilibrium involving gases at high pressure.

G = RT ln f + θ-------------(1)

where G= Gibbs free energy 1 mole

R = Gas const , T = abs Tempr

θ= function of tempr.

diff eqn.(1) at const tempr , dq= RTd Inf-------(2)

WKT dq=vdp-SdT

At const T, dq= vdp-------------(3)

comparing (2) & (3), we get

RTdInf = vdp------------(4)

Fugacity for ideal gas:- Consider RtdInf = vdp => RTdInf = RT/P * dp

=> dInf = dInp  or f=p for ideal gas

f=p for non- ideal gas.

Fugacity is a intensive property & in a measure of compositon of gases.

Fugacity has the same dimension or pressure, usually atm or bar.

Fugacity co-efficent ( Φ ):- is defined as the ratio of fugacity of Φ component toits pressure  Φ = f/p

for ideal gas, Φ=1 , for non – ideal gases Φ = 1

Φ is a measure of non- ideal behavior of a gas .