Thermodynamics – Chemistry Study Notes

Fundamental Concepts and Thermodynamic Processes

To understand thermodynamics, we must first define the boundaries between a system (the part of the universe under observation) and its surroundings (the rest of the universe).

Systems are classified as open (exchange of mass and energy), closed (exchange of energy only), or isolated (no exchange of mass or energy).

The state of a system is defined by macroscopic properties like pressure, volume, temperature, and composition. These are categorized into extensive properties (depend on the amount of matter, e.g., mass, volume, enthalpy) and intensive properties (independent of the amount of matter, e.g., temperature, density, pressure).

Thermodynamic processes describe how a system transitions from one equilibrium state to another. These processes are foundational for numerical problems in JEE and NEET:

• Isothermal Process: Temperature remains constant ($\Delta T = 0$, $\Delta U = 0$ for an ideal gas). Heat exchange occurs freely with the surroundings.
• Adiabatic Process: No heat is exchanged with the surroundings ($q = 0$). Systems undergo expansion or compression resulting in temperature changes.
• Isobaric Process: Pressure remains constant ($\Delta P = 0$). Volume and temperature vary proportionally.
• Isochoric Process: Volume remains constant ($\Delta V = 0$), implying that no pressure-volume work is done ($w = 0$).

Cyclic processes return the system to its initial state.

This means that the change in any state function (like internal energy or enthalpy) over a complete cycle is identically zero ($\oint dU = 0$).

First Law of Thermodynamics and Work Done

The First Law of Thermodynamics is essentially the law of conservation of energy applied to thermodynamic systems. It states that the energy of an isolated system is constant, though it can be transformed from one form to another.

Mathematically, it is expressed as $\Delta U = q + w$, where $\Delta U$ is the change in internal energy, $q$ is the heat absorbed by the system, and $w$ is the work done on the system according to IUPAC sign conventions.

“Work done on the system is positive ($+w$), while work done by the system is negative ($-w$). Similarly, heat absorbed by the system is positive ($+q$), and heat released by the system is negative ($-q$).”

Calculating the work done ($w$) varies depending on the nature of the process:

• Isothermal Reversible Expansion: $w = -nRT \ln\left(\frac{V_f}{V_i}\right) = -2.303 nRT \log\left(\frac{P_i}{P_f}\right)$
• Isobaric Process: $w = -P_{\text{ext}}(V_f – V_i)$
• Isochoric Process: $w = 0$ because $\Delta V = 0$.
• Adiabatic Reversible Process: $w = \frac{P_2V_2 – P_1V_1}{\gamma – 1} = \frac{n R (T_2 – T_1)}{\gamma – 1} = n C_v (T_2 – T_1)$

Enthalpy ($H$) is defined as a state function representing total heat content at constant pressure: $H = U + PV$.

For an ideal gas, the relationship between molar heat capacities at constant pressure ($C_p$) and constant volume ($C_v$) is given by the famous Mayer’s relation: $C_p – C_v = R$, where $\gamma = \frac{C_p}{C_v}$ is the heat capacity ratio.

Second and Third Laws of Thermodynamics

While the first law tracks energy conservation, it cannot predict the direction of a process. This limitation is overcome by the Second Law of Thermodynamics.

It states that the total entropy of an isolated system must increase for any spontaneous process: $\Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surrounding}} > 0$.

Entropy ($S$) is a measure of molecular disorder or randomness. For a reversible process, entropy change is defined as $\Delta S = \int \frac{dq_{\text{rev}}}{T}$.

For an ideal gas undergoing a state change, the entropy change is calculated using the formula:

$$\Delta S_{\text{system}} = n C_v \ln\left(\frac{T_2}{T_1}\right) + n R \ln\left(\frac{V_2}{V_1}\right)$$

The Third Law of Thermodynamics states that the entropy of a perfectly crystalline solid approaches zero as the temperature approaches absolute zero ($T \to 0\text{ K}$). This provides an absolute reference scale for determining experimental entropies of chemical substances.

Gibbs Free Energy and Spontaneity Criteria

To evaluate spontaneity without calculating the entropy of the surroundings every time, scientists use Gibbs Free Energy ($G$), defined as $G = H – TS$.

At constant temperature and pressure, the change in Gibbs free energy determines whether a process is spontaneous:

• $\Delta G < 0$ (Negative): The process is spontaneous and exergonic.
• $\Delta G > 0$ (Positive): The process is non-spontaneous and endergonic.
• $\Delta G = 0$ (Zero): The system is at equilibrium.

The master equation governing temperature dependence of Gibbs free energy is $\Delta G = \Delta H – T\Delta S$. The sign of $\Delta G$ depends heavily on the signs of $\Delta H$ and $\Delta S$ at varying temperatures.

Furthermore, standard free energy change is related to the equilibrium constant ($K$) via the equation: $\Delta G^\circ = -RT \ln K = -2.303 RT \log K$.

Important Facts / Formulas

Key Points to Remember

• State functions (like $U$, $H$, $S$, $G$, $P$, $V$, $T$) depend only on the initial and final states, not on the path taken.
• Work ($w$) and heat ($q$) are path functions, meaning their values depend entirely on the manner in which the process is conducted.
• In free expansion of an ideal gas into a vacuum against $P_{\text{ext}} = 0$, both work done and heat exchange are zero ($w = 0, q = 0, \Delta U = 0, \Delta T = 0$).
• For an isothermal irreversible process against a constant external pressure, calculate $w = -P_{\text{ext}}(V_2 – V_1)$, not the logarithmic reversible formula.
• Standard enthalpy of formation ($\Delta_f H^\circ$) of an element in its most stable allotropic state at $298\text{ K}$ and $1\text{ atm}$ is defined as zero.
• Equipartition of energy states that internal energy for an ideal gas is given by $U = \frac{f}{2} nRT$, where $f$ is the degree of freedom.
• Entropy increases during phase transitions like melting, vaporization, and sublimation, as well as during expansions and mixing of gases.

Previous Year Question Hints

• Hint 1: When a question asks for the maximum work obtainable in an isothermal expansion, always apply the reversible work formula: $w_{\text{max}} = -2.303 nRT \log(V_2/V_1)$.
• Hint 2: To find the temperature at which a non-spontaneous reaction becomes spontaneous ($\Delta H > 0, \Delta S > 0$), set $\Delta G = 0$ to get $T = \frac{\Delta H}{\Delta S}$, then check the inequality condition for negative $\Delta G$.
• Hint 3: Watch out for units! Gas constant $R = 8.314\text{ J K}^{-1}\text{mol}^{-1}$ should be paired with joules, while $R = 2\text{ cal K}^{-1}\text{mol}^{-1}$ is used when working with calories.

Quick Revision Summary

• Thermodynamics distinguishes between open, closed, and isolated systems, utilizing state and path functions.
• The First Law establishes energy conservation through $\Delta U = q + w$.
• Heat capacities are linked via $C_p – C_v = R$ for ideal gases, with $\gamma = C_p/C_v$ controlling adiabatic indexes.
• Work calculations depend on whether the process is isothermal, isobaric, isochoric, or adiabatic, and whether it runs reversibly or irreversibly.
• The Second Law introduces entropy ($\Delta S$) as a driving force for spontaneity in isolated systems.
• Gibbs free energy ($\Delta G = \Delta H – T\Delta S$) combines system enthalpy and entropy to serve as the ultimate criteria for reaction spontaneity.
• Standard free energy changes tie thermodynamics directly to chemical equilibrium constants ($K$).
• Third law assigns zero entropy to pure crystalline solids at absolute zero temperature.