For the case of an isothermal processes since temperature is constant the above equation will simplify to

∆S

where q rev, refers to the total heat change in going from state A to state B Isothermally SinceUnivariate……….. is an isothermal process &reversible processes too above equation can be used .

Entropy changes with Temperature variation in homogeneous systems

(a)Under isochoric conditionsRemember we proved that if no work other than PV work occur heat change at constant volume dqv=du

ʽdu’ is a thermodynamic property dqvmust be a T.D .property.

dqvshould be equaled to heat change under reversible condition. :i.e =rev

= nCvmdT =

∆S= = nCv,m

=nCv ,m

(b)Under isobaric condition= if no work other than P-V work occurs is a thermodynamic property is independent of path & has the same value of initial & final states are the same . it should be equal to

= =nCpm

=nCp ,m

==0 for a reversible and adiabatic processes

Irrespective of the value of Temperature

The concept of Gibbs Free energy

• Spontaneity of a process in a closed system ultimately is determined by two factors .They are ,

1. Energy factors 2. Entropy factorsTherefore it is useful to combine these 2 factors and define a new extensive thermodynamic property (funtions) that can be used to predict spontaneity of a process . Occurs at [T]&[P]The new extensive thermodynamic property is called Gibb Free Energy(G),is defined as G = H - TS

ALTERNATIVE FORMULATION OF THE SECOND LAW• Gibbs Free Energy Criterion for Equilibrium & Spontaneity of a

system For a closed system at constant temperature & constant pressurei. for a spontaneous process ii. =0 for rev. process iii. for a non spontaneous process

Entropy Entropy change for isothermal process in ideal gasesit was proved before that the internal energy & enthalpy of ideal gases do not depend on their volume and pressure. Further it was shown that they depend only on Temperature .for ideal gases undergoing isothermal changes ,

Since It follows that for an ideal gas, undergoing an isothermal change q= -w =It has already been proved that the work done on `n’ mole of an ideal gas undergoing a reversible change around a volume V1 to V2 at constant Temperature T is given by W rev =nRT

The heat absorbed by n moles of an ideal gas undergoing a reversible change from volume V1 to V2 as constant Temperatureis given by

q rev = (-)w rev = nRT

since P1V1=P2V2

Thecorresponding isothermal entropy change at Temperature T,is