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Thermodynamic Equations Of State | Physical Chemistry PDF Download
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)
Accordingly,
and 
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)
then 
⇒ 
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 
Hence, 
Internal energy change
We know that,
∴
(at constant temperature)
Enthalpy change
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
and 
If V >> nb, than
Hence,
Since for the expansio n of a gas, V2 > V1 then
Wideal > Wreal
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FAQs on Thermodynamic Equations Of State - Physical Chemistry
| 1. What are thermodynamic equations of state? |  |
Ans. Thermodynamic equations of state are mathematical relationships that describe the behavior of a system in terms of its properties, such as temperature, pressure, volume, and composition. These equations provide a quantitative description of the relationship between these properties, allowing us to predict and analyze the thermodynamic behavior of a system.
| 2. What is the significance of equations of state in thermodynamics? | |
Ans. Equations of state play a crucial role in thermodynamics as they provide a mathematical framework to describe and analyze the behavior of fluids and gases. These equations allow us to calculate and predict the thermodynamic properties of a system, such as its pressure, volume, and temperature, under different conditions. They are essential tools in various applications, including engineering, chemistry, and physics.
| 3. What are some commonly used equations of state? | |
Ans. There are several commonly used equations of state in thermodynamics, including:
- Ideal Gas Law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
- Van der Waals Equation: (P + an^2/V^2)(V - nb) = nRT, where a and b are constants that account for the attractive and repulsive forces between gas molecules.
- Redlich-Kwong Equation: P = (RT)/(V - b) - a/(sqrt(T)V(V + b)), where a and b are constants specific to each gas.
- Peng-Robinson Equation: P = (RT)/(V - b) - (aα)/(V(V + b) + b(V - b)), where a and b are constants and α is a temperature-dependent parameter.
- Soave-Redlich-Kwong Equation: P = (RT)/(V - b) - (aα)/(V(V + b)), where a and b are constants and α is a temperature-dependent parameter.
| 4. How are equations of state derived? | |
Ans. Equations of state are derived based on empirical observations and theoretical models. The derivation often involves making assumptions about the behavior of the system and applying mathematical techniques, such as calculus and statistical mechanics. Some equations of state are derived from first principles, while others are developed by fitting experimental data. The accuracy and applicability of an equation of state depend on the specific system and conditions it is designed to describe.
| 5. Can equations of state be used for any system or substance? | |
Ans. Equations of state are formulated to describe the behavior of specific systems or substances. Different equations of state may be required for different types of systems, such as ideal gases, real gases, or liquids. The choice of equation of state depends on the properties of the system and the level of accuracy required. It is important to select an appropriate equation of state that is applicable to the specific conditions and substances being studied to ensure accurate predictions and analysis.
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