Question

Under what conditions is change in work function equal to change in Gibbs free energy, i.e. \(\Delta \mathrm{A}=\Delta G\) (a) When there is no change in volume, i.e. \(\Delta V=0\) (b) When there is no change in enthalpy, i.e. \(\Delta H=0\) (c) When there is no change in temperature (d) When there is no change in pressure

Short answer

The change in work function is equal to the change in Gibbs free energy when there is no change in temperature.

Step-by-step solution

Analyze the given options

It's understood that the work function and the Gibbs free energy are related, and when conditions change they equal. Let's analyze each of the conditions provided to determine if they maintain the equilibrium.

Evaluate Option (a)

When \(\Delta V = 0\), it means that there is no change in volume. However, Gibbs free energy (\(G\)), according to its formula \(G = H - TS\), is not directly correlated with volume. Therefore, a change in Gibbs free energy does not necessarily imply a change in the work function under this condition. So, option (a) is not correct.

Evaluate Option (b)

When \(\Delta H = 0\), it means that there is no change in enthalpy. However, enthalpy (\(H\)) is a part of the Gibbs free energy, but it's not the sole variable. So, the enthalpy change being zero doesn't mean \(\Delta A = \Delta G\), as the entropy and temperature could still cause changes. Therefore, option (b) is not correct.

Evaluate Option (c)

When there is no change in temperature, \(\delta Q = \Delta U + P \Delta V\), where \(\delta Q\) denotes heat transfer, \(\Delta U\) change in internal energy and \(P \Delta V\) work done by the system. If the temperature is constant, then all changes are due to work done by the system. This means that \(\Delta A = \Delta G\). Therefore, option (c) is correct.

Evaluate Option (d)

When there is no change in pressure, the Gibbs free energy does not necessarily remain constant since it is also dependent on entropy and temperature. So, even if the pressure is constant, other contributing factors may still cause a change in Gibbs free energy that does not equal a change in the work function. Therefore, option (d) is not correct.

Key concepts

Work Function

The work function, often symbolized as \(\), is a term commonly used in thermodynamics and physics. It represents the minimum energy needed to remove an electron from the surface of a material to a point just outside a material, which is an important concept in fields like photoelectric effects. In the context of thermodynamic processes, the work function can also resemble the Helmholtz Free Energy. It is the useful work obtainable from a constant volume, constant temperature system.
It's vitally important in understanding how energy transfer occurs without a change in volume, as it describes a process where the system does not perform work on the surroundings by way of expansion or contraction. The work function thus becomes crucial when defining conditions where a process's efficiency or reversibility is considered. In simpler terms, when analyzing changes in a system, the work function helps us determine how much of an energy input is actually useful for doing work.

Enthalpy

Enthalpy, designated as \(\), is a key concept in thermodynamics, calculating the total heat content of a system. It's defined as the sum of the internal energy of the system plus the product of pressure \(\times\) volume, i.e., \(H = U + PV\).
One of the core uses of enthalpy is in processes where pressure remains constant, making it extremely useful in chemical reactions, phase changes, and heat transfer analysis. Understanding \(\Delta H\) or change in enthalpy is essential in predicting whether a reaction will be endothermic (absorbing heat) or exothermic (releasing heat). For instance, the combustion of wood releases energy, indicating a negative enthalpy change.

• Endothermic process: Absorbs heat, \(\Delta H > 0\)
• Exothermic process: Releases heat, \(\Delta H < 0\)

Knowing the change in enthalpy allows for better predictions of energy exchanges and can help gauge reaction feasibility under specified thermal conditions.

Entropy

Entropy, denoted \(\), is a measure of disorder or randomness in a system and is a fundamental concept intertwined with the second law of thermodynamics which states that the entropy of an isolated system always increases over time. In the context of Gibbs Free Energy, entropy plays a critical role because Gibbs Free Energy \(G\) is defined as \(G = H - TS\). This equation highlights the balance between enthalpy \(H\), entropy \(S\), and temperature \(T\).
Higher entropy indicates greater disorder and more ways energy can be distributed within a system, making it a vital consideration in reactions and processes. It explains why certain processes, although energetically feasible, do not occur spontaneously, due to entropic limitations. For reactions, a key takeaway is:

• Higher entropy contributes to the feasibility of processes, making unfavorable (endothermic) reactions feasible under high temperature.
• Reactions that lead to an increase in entropy are generally more likely to occur.

Understanding changes in \(\Delta S\) helps decipher the directionality and progression rate of chemical processes.

Thermodynamic Equilibrium

Thermodynamic equilibrium is a state where a system's macroscopic properties do not change over time, and there are no net flows of matter or energy. It encompasses three types of equilibrium: thermal, chemical, and mechanical.

• Thermal equilibrium occurs when temperature is uniform throughout the system, ensuring no net heat flow.
• Chemical equilibrium exists when the chemical composition remains constant over time, synonymous with a state where forward and reverse reaction rates are equal.
• Mechanical equilibrium involves no unbalanced forces within the system, implying that the pressure is uniform across the system.

An important concept regarding thermodynamic equilibrium is that a system in this state maximizes its entropy. It signifies conditions where the Gibbs Free Energy is minimized for a constant temperature and pressure system, aligning with the most stable configuration. This state is critical in understanding how energy efficiencies can be achieved in processes such as energy conversion systems, refrigeration, and chemical reaction pathways.