Calculating Gibbs Free Energy for Adiabatic Irreversible Expansion of a Gas

For an adiabatic irreversible expansion of a gas, the change in Gibbs free energy, denoted as ΔG, is not indeterminate. It can be determined using specific thermodynamic relationships under certain conditions. This article will delve into the factors influencing ΔG, the definitions and key points regarding Gibbs free energy, and the practical steps to calculate it for an adiabatic and irreversible expansion.

Understanding Gibbs Free Energy

The Gibbs free energy, denoted as G, is a thermodynamic potential that measures the maximum reversible work that can be extracted from a system at constant temperature and pressure. The definition of Gibbs free energy is given by the equation:

G H - TS

H is the enthalpy of the system. T is the temperature of the system. S is the entropy of the system.

Irreversible Processes and Thermodynamic Equilibrium

Fundamentally, irreversible processes are characterized by the fact that the system does not remain in thermodynamic equilibrium. This means that the Gibbs free energy change cannot be calculated directly using standard equilibrium relationships. However, even in irreversible processes, the change in Gibbs free energy (ΔG) can be determined. This is because state functions like free energy and entropy are path-independent.

Adiabatic Processes

Adiabatic processes are those in which there is no heat exchange with the surroundings (Q 0). For an ideal gas, if there is no heat exchange, the internal energy change (ΔU) is equal to the work done on or by the system. In such processes, the relationship between the change in Gibbs free energy (ΔG), change in enthalpy (ΔH), and change in entropy (ΔS) is given by:

ΔG ΔH - TΔS

Practical Calculation Steps

To calculate the change in Gibbs free energy (ΔG) during an adiabatic irreversible expansion, the initial and final states of the gas (pressure, temperature, and volume) must be known. Here are the steps to follow:

Calculate the change in enthalpy (ΔH) using the temperature change (ΔT) if the process involves an ideal gas. The change in enthalpy for an ideal gas can be approximated using:

ΔH CpΔT

Where Cp is the molar heat capacity at constant pressure.

Derive the change in entropy (ΔS) from the relationship between the irreversible process and the entropy change.

For an adiabatic process, the relationship between the entropy change (ΔS) and the volume change (ΔV) can be expressed as:

ΔS nR ln(V2/V1)

Where n is the number of moles, R is the universal gas constant, and V1 and V2 are the initial and final volumes, respectively.

Substitute the calculated ΔH and ΔS values into the equation for ΔG:

ΔG ΔH - TΔS

Conclusion

Although the change in Gibbs free energy during an irreversible adiabatic expansion can be more complex to calculate than in reversible processes, it is not indeterminate. It can be calculated from the appropriate thermodynamic relationships if the initial and final states are known. By understanding the principles of Gibbs free energy, adiabatic processes, and the path-independent nature of state functions, one can accurately determine the change in Gibbs free energy for such expansions.

Further reading will help solidify these concepts and provide additional insights into thermodynamics and irreversible processes.

References:

Wikipedia - Gibbs Free Energy LibreTexts - Reversible and Irreversible Processes and Free Energy