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1. Sayem Shaikh
Roll No.5
Physical chemistry presentation
● Topic:::State function
----Exact differential.
—-Maxwell equation and relation,significance
and application to ideal gas
—-Joule-Thomson experiment,it's Coefficient,
Coefficient in terms of Vander der Walls
constant,
—-Inversion temperature

2. State Function
● A state function is any thermodynamic property whose
value for the process is independent of the path.
● It depends only on the state of the system (in terms of
state variables like P, V, T, n,U), not on its history or how
the system got to that state.
● A thermodynamic property whose value for the process
does depend on the path is not a state function.
● State functions are symbolized by capital letters; non-state
functions are symbolized by lowercase letters. Internal
energy is a state function. Work and heat are not.

4. ● As you see,cyclic integration of
dU is zero.Thus,U is a state
function.
● Exact differential shown
only by state functions.
● State functions follow
Euler’s theorem
● Cyclic integration of state
functions are always zero.

5. Exact differential
● State functions actually show exact differential.
● If a function is exact differential that means it is a
state function
● Exact differential condition is obtain from Euler's
theorem.
●

6. ● Let suppose we have a thermodynamic relation
● Maxwell Relations says that both side are actually
equal.
● That means, dH is an exact differential and H is a
state function.

7. Maxwell Relations
● Maxwell Equation relates
different thermodynamic para-
meters
● All this are derived from euler-
reciprocity equation.
● These Maxwell Relations not
restricted to ideal gases or just
gases,they are applicable to
solid and liquid system as well.

8. ● They express some relation in terms of variables
that are easy to measure.
● Certain variables in thermodynamic are difficult to
measure experimentally like S and some are
easier to measure like T and P.
● By using Maxwell relation we can relate entropy
with easier variables.
● Example.

9. ● Thermodynamic square helps to forms Maxwell
Relations.

10. Application to ideal gas

11. Joule-Thomson Experiment
● An adiabatic system is set
up and filled with a gas on
one side of the porous
barrier.
● This gas has some T1,
some fixed pressure P1,
and initial volume V1.
● A piston pushes on the gas
and pushes all of it through
the barrier,so the final
volume on this side become
zero.

12. ● On the other side of the barrier, a second piston moves out
as the gas diffuses to the other side, where it will have a
temperature T2, a fixed pressure p2, and a volume V2.
● Initially, the volume on the right side of the barrier is zero.
● Since the gas is being forced through a barrier, it is
understood that p1 >p2.
● On the left side, work is done on the gas, which
contributes positively to the overall change in energy.
● On the right side, the gas does work, contributing
negatively to the overall change in energy.
● The net work Wnet performed by the system after the first
piston is completely pushed in is
Wnet =p1V1-p2V2

13. Joule-Thomson Coefficient
● Since,the system is adiabatic,q=0 so,∆Unet=Wnet
● Internal energy change is from U1 to U2
● Therefore,. Wnet=U2-U1
● Equation two equations,
P1V1-P2V2=U2-U1
U1+P1V1=U2+P2V2
H1=H2
● Therefore,∆H=0
● Since, enthalpy of the gas does not change,the
process is called isenthalpic process.

14. ● Although,the change in enthalpy is zero,the
change in temperature not.
● Joule-Thomson Coefficient defined as change in
T of a gas with pressure at contant enthalpy.
● For,ideal gases
μJT=0,since enthalpy
depend only on temperature.

15. J-T Coefficient in terms of Van
der Walls constant
j

16. Inversion Temperature
● The temperature below which a gas becomes cooler
on expansion is known as Inversion Temperature.
● Under some condition J-T Coefficient is -ve, meaning
as P decrease T goes up.
● It gets hotter on expansion.
● At some lower T,J-T Coefficient become +ve,means
as P dropes T drops too.
● In order to cool gas,the T must be below inversion
temperature.
● Inversion temperature of hydrogen is -48°C and
helium is -242°C.

17. ● Joule-Thomson effect can also be known as
Throttling effect.

18. Reference
● Physical chemistry by David W.Ball
● Physical chemistry by Puri,Sharma,pathania.
● Website help
● Visual help from YouTube

19. Thank you all
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