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Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Document Description: Thermodynamic Equations Of State for GRE 2022 is part of Chemistry for GRE Paper II preparation. The notes and questions for Thermodynamic Equations Of State have been prepared according to the GRE exam syllabus. Information about Thermodynamic Equations Of State covers topics like and Thermodynamic Equations Of State Example, for GRE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Thermodynamic Equations Of State.

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Thermodynamic equation of state:

(1)   First thermodynamic equation of state: The charge in internal energy with respect to volume at constant temperature is known as first thermodynamic equation of state. i.e.

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Dimensionally it is equal to pressure.  Thus it is also called internal pressure (π).
We know that

Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
dU = TdS – PdV

∴  Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE                     Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

 

(2)  Second thermodynamic equation of state: The change in enthalpy w.r.t. pressure at constant temperature is known as second thermodynamic equation of state.

dH = TdS + VdP

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE                     Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Comparison of Isothermal and Adiabatic Expansions: Let us consider isothermal and adiabatic expansio ns of an ideal gas from initial volume Vi and pressure Pi to a commo n final vo lume Vf.  If Piso and Padia are final pressure, then

PiVi = Piso Vf                               (for isothermal expansio n)
and PiVi r = Padia Vf r                (for adiabat ic expansio n)
Accordingly,

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
and Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

 

Since for expansio n Vf > Vi and for all r > 1, hence

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE


Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GREThermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

From graph (a) & (b), it is clear that work done in isothermal expansion (shown by area ABCD) is greater than the work done in adiabatic expansion (shown by area AECD).
Consider the expansions in which the final pressure Pf is the same in both cases.  If Viso and Vadia are the final volume is isothermal and adiabatic expansion then

PiVi = Pf Viso                        (for isothermal expansion)
and Pi Vir = Pf Vadia                     (for adiabatic expansion)
then Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
⇒         Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

or Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE                 [∵ r > 1 then]
Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GREor     Vadia < Viso

 

Reversible Isothermal expansion of a Real gas Using vendor walls equation we find the expression for W, ΔV, ΔH and q for reversible isothermal expansion of real gas.

Work of expansion

Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

For the vendor walls gas,

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE= nRT so that Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE


Hence,        Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE


Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE


Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Internal energy change

We know that,

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE                      (at constant temperature)
Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Enthalpy change

Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Heat change. We know that ΔU = q + w or q = ΔU - w
Subst ituting the value of w & ΔU in this equation we get

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Comparison of Work of Expansion of an ideal gas and a real gas.
We know that

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE
and Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

If  V >> nb, than

Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Hence, 

 Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE

Since for the expansio n of a gas, V2 > V1 then
Wideal > Wreal

The document Thermodynamic Equations Of State Notes | Study Chemistry for GRE Paper II - GRE is a part of the GRE Course Chemistry for GRE Paper II.
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