Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

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Chemistry : Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

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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 Equation Of State - Thermodynamic Chemistry Notes | EduRev

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

Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev
dU = TdS – PdV

∴  Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev                     Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

 

(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 Equation Of State - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev                     Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

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 Equation Of State - Thermodynamic Chemistry Notes | EduRev
and Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

 

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

 Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev


Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRevThermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

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 Equation Of State - Thermodynamic Chemistry Notes | EduRev
⇒         Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

or Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev                 [∵ r > 1 then]
Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRevor     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 Equation Of State - Thermodynamic Chemistry Notes | EduRev

For the vendor walls gas,

 Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev= nRT so that Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev


Hence,        Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev


Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev


Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

Internal energy change

We know that,

 Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev                      (at constant temperature)
Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

Enthalpy change

Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

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 Equation Of State - Thermodynamic Chemistry Notes | EduRev

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

 Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev
and Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

If  V >> nb, than

Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

Hence, 

 Thermodynamic Equation Of State - Thermodynamic Chemistry Notes | EduRev

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

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