Unit 2: Chemical Thermodynamics II
Course: CHM-DSC-251
Institution: Assam University, Silchar
Table of Contents
1. Second Law of Thermodynamics & Entropy
While the First Law focuses on energy conservation, the Second Law determines the direction of spontaneous change.
Limitations of the First Law
The First Law cannot explain why certain processes occur spontaneously in one direction but not the reverse (e.g., heat flowing from hot to cold).
Concept of Entropy (S)
Entropy is a measure of the molecular disorder or randomness of a system. It is a state function.
Mathematical expression for entropy change: dS = dq_rev / T
For a reversible process, the entropy change of the universe is zero. For an irreversible (spontaneous) process, the entropy of the universe increases.
2. Clausius Inequality
The Clausius Inequality provides a mathematical criterion for the spontaneity of a process.
dS ≥ dq / T
- dS = dq_rev / T: For a reversible process.
- dS > dq_irrev / T: For an irreversible/spontaneous process.
3. Free Energy Functions (Gibbs & Helmholtz)
To predict spontaneity without checking the entire universe, we use system-specific functions: Gibbs Free Energy (G) and Helmholtz Free Energy (A).
| Function | Definition | Condition |
|---|---|---|
| Helmholtz Energy (A) | A = U - TS | Constant Temperature and Volume |
| Gibbs Energy (G) | G = H - TS | Constant Temperature and Pressure |
4. Spontaneity and Equilibrium
The criteria for spontaneity based on free energy changes are vital for chemical reactions.
- ΔG < 0: Spontaneous process.
- ΔG = 0: System at equilibrium.
- ΔG > 0: Non-spontaneous process.
Gibbs-Helmholtz Equation
This equation relates the temperature dependence of Gibbs energy to enthalpy.
[d(G/T) / dT]_P = -H / T²
5. Maxwell Relations & Thermodynamic Equations
Maxwell relations allow us to relate non-measurable quantities (like entropy) to measurable ones (P, V, T).
Common Maxwell Relations derived from exact differentials:
- (dS/dV)_T = (dP/dT)_V
- (dS/dP)_T = -(dV/dT)_P
6. Joule-Thomson Coefficient (μ_JT)
The Joule-Thomson effect describes the temperature change of a real gas when it expands through a porous plug into a lower pressure region under adiabatic conditions.
μ_JT = (dT / dP)_H
For an ideal gas, μ_JT = 0 because there are no intermolecular forces to overcome.
7. Exam Focus Section
Exam Tips- Entropy Calculation: Be prepared to calculate ΔS for phase transitions (ΔS = ΔH_vap/T) and for ideal gas expansion.
- Signs of ΔG: Always check if the question specifies "constant P and T" before using ΔG as a spontaneity criterion.
- Derivations: Practice deriving Maxwell relations from the fundamental equations (dU, dH, dG, dA).
Q: Why is the Second Law necessary if we have the First Law?
A: The First Law only tracks energy quantity. The Second Law tracks energy quality and directionality.
Q: What is the physical significance of ΔA?
A: It represents the maximum work (reversible work) a system can perform at constant T and V.
- Using ΔG to predict spontaneity for processes not occurring at constant T and P.
- Forgetting that entropy must increase for the Universe (System + Surroundings), not just the system.