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.
Dimensionally it is equal to pressure. Thus it is also called internal pressure (π).
We know that
dU = TdS – PdV
(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
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)
Since for expansio n Vf > Vi and for all r > 1, hence
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)
or [∵ r > 1 then]
or 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
For the vendor walls gas,
= nRT so that
Internal energy change
We know that,
∴ (at constant temperature)
Heat change. We know that ΔU = q + w or q = ΔU - w
Subst ituting the value of w & ΔU in this equation we get
Comparison of Work of Expansion of an ideal gas and a real gas.
We know that
If V >> nb, than
Since for the expansio n of a gas, V2 > V1 then
Wideal > Wreal