7.1 Entropy change of pure substances

Entropy change in pure substances is a key concept in thermodynamics. It helps us understand how disorder changes during processes like heating, cooling, and phase transitions. This knowledge is crucial for predicting spontaneous reactions and energy flow.

Calculating entropy changes involves looking at heat transfer and temperature changes. For different processes like isothermal or isobaric, we use specific equations. Understanding these calculations is essential for applying entropy concepts to real-world problems.

Entropy in Thermodynamics

Definition and Significance

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• Entropy measures the disorder or randomness of a system
• Entropy is a state function depending only on the initial and final states of the system
• Entropy helps determine the direction of spontaneous processes and the maximum work that can be extracted from a system
• The entropy of a system increases when heat is added and decreases when heat is removed, provided the temperature remains constant
• In an isolated system, entropy always increases or remains constant, never decreasing (second law of thermodynamics)
• The unit of entropy is joules per kelvin (J/K) in the SI system

Relationship with Heat and Temperature

• Entropy change is directly proportional to the heat transferred reversibly and inversely proportional to the absolute temperature ([ΔS = ∫(dQ/T)](https://www.fiveableKeyTerm:δs_=_∫(dq/t)))
• Adding heat to a system at a constant temperature increases its entropy, while removing heat decreases its entropy
• Systems with higher temperatures have a greater capacity for entropy changes when heat is transferred (lower $ΔS$ for a given $dQ$)

Calculating Entropy Changes

Pure Substances and Various Processes

• The entropy change of a pure substance can be calculated using the equation $ΔS = ∫(dQ/T)$, where $dQ$ is the heat transferred reversibly and $T$ is the absolute temperature
• For an isothermal process, the entropy change is given by [ΔS = Q/T](https://www.fiveableKeyTerm:δs_=_q/t), where $Q$ is the heat transferred and $T$ is the constant absolute temperature
• In an isobaric process, the entropy change can be calculated using the specific heat capacity at constant pressure ($c_p$) and the equation $ΔS = c_p × ln(T_2/T_1)$, where $T_1$ and $T_2$ are the initial and final absolute temperatures, respectively
• For an isochoric process, the entropy change is zero, as no heat is exchanged with the surroundings ($dQ = 0$)

Phase Transitions and Entropy Changes

• The entropy change during a phase transition (melting or vaporization) at constant temperature is given by $ΔS = ΔH/T$
• $ΔH$ is the enthalpy of the phase transition and $T$ is the absolute temperature at which the transition occurs
• Phase transitions involve a significant increase in entropy due to the increased disorder of the system (solid to liquid or liquid to gas)
• The entropy of vaporization is generally greater than the entropy of fusion for a given substance, as gases have more disorder than liquids

Entropy and the Second Law

Spontaneous Processes and Irreversibility

• The second law of thermodynamics states that the total entropy of an isolated system always increases over time, or remains constant in the case of a reversible process
• In any spontaneous process, the entropy of the universe (system + surroundings) increases, indicating the natural direction of the process
• The second law introduces the concept of irreversibility, as the entropy of an isolated system cannot decrease without external intervention

Clausius Inequality

• The Clausius inequality ($ΔS ≥ ∫(dQ/T)$) is a mathematical representation of the second law of thermodynamics
• It shows that the entropy change of a system is always greater than or equal to the heat exchanged reversibly divided by the absolute temperature
• For reversible processes, the Clausius inequality becomes an equality ($ΔS = ∫(dQ/T)$), while for irreversible processes, it is a strict inequality ($ΔS > ∫(dQ/T)$)

Reversible vs Irreversible Processes

Characteristics of Reversible Processes

• A reversible process is one in which the system and its surroundings can be restored to their original states without any net change in the entropy of the universe
• In a reversible process, the entropy change of the system is equal to the heat exchanged reversibly divided by the absolute temperature ($ΔS = ∫(dQ/T)$)
• Reversible processes are idealized and cannot be achieved in practice due to factors such as friction, heat loss, and non-equilibrium conditions
• Examples of reversible processes include isothermal expansion or compression of an ideal gas, and phase transitions at constant temperature and pressure

Characteristics of Irreversible Processes

• An irreversible process is one in which the system and its surroundings cannot be restored to their original states without a net increase in the entropy of the universe
• In an irreversible process, the entropy change of the system is always greater than the heat exchanged reversibly divided by the absolute temperature ($ΔS > ∫(dQ/T)$), as stated by the Clausius inequality
• Most real-world processes are irreversible due to factors such as friction, heat loss, and non-equilibrium conditions
• Examples of irreversible processes include spontaneous heat transfer from a hot object to a cold object, the expansion of a gas into a vacuum, and the mixing of two different substances (diffusion)