Question

Which of the following thermodynamic functions are associated only with the first law of thermodynamics: \(S, U, G,\) and \(H ?\)

Short answer

The internal energy \( U \) is associated only with the first law of thermodynamics.

Step-by-step solution

Understanding the First Law of Thermodynamics

The first law of thermodynamics is expressed as \( \Delta U = Q - W \), where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system. This law emphasizes the conservation of energy and is primarily concerned with changes in internal energy, \( U \).

Identifying Thermodynamic Functions

The thermodynamic functions given are: entropy \( S \), internal energy \( U \), Gibbs free energy \( G \), and enthalpy \( H \). We need to determine which of these functions are directly related to the first law of thermodynamics.

Analyzing Each Function

Internal energy \( U \) is directly related to the first law, as it describes energy changes within a system. The first law equation \( \Delta U = Q - W \) is specifically about changes in \( U \). Entropy \( S \), Gibbs free energy \( G \), and enthalpy \( H \) involve other laws or conditions of thermodynamics, such as the second law and conditions of constant pressure or temperature.

Conclusion

Given the analysis, the function associated only with the first law is internal energy \( U \). The other functions may involve additional thermodynamic laws or are derived from specific conditions that extend beyond the first law.

Key concepts

Internal Energy

Internal energy, often denoted by the symbol \( U \), is a core concept of the first law of thermodynamics. This law is succinctly presented by the equation \( \Delta U = Q - W \). Here, \( \Delta U \) refers to the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.
Internal energy represents the total energy contained within a system, encompassing kinetic and potential energies at the molecular level. It does not include macroscopic kinetic or potential energy.
To understand internal energy better:

• It is an extensive property, meaning it depends on the size or extent of the system.
• It changes as energy is transferred in the form of heat or work.
• Only differences in internal energy can be measured directly.

Internal energy is fundamental to the study of thermodynamics, as it provides insight into how energy is conserved and transformed within a system.

Thermodynamic Functions

Thermodynamic functions are properties used to describe the state and behavior of a system in thermodynamics. The main functions include:

• Entropy \( S \)
• Internal energy \( U \)
• Gibbs free energy \( G \)
• Enthalpy \( H \)

Each of these functions serves a unique purpose, often related through different laws of thermodynamics.While internal energy \( U \) is solely associated with the first law of thermodynamics, the other functions are related to or derived from additional thermodynamic principles:

• Entropy \( S \): Involves the second law of thermodynamics and measures the level of disorder or randomness in a system.
• Gibbs free energy \( G \): Useful for predicting the direction of chemical processes and reactions under constant pressure and temperature.
• Enthalpy \( H \): Represents the total heat content and is particularly useful in processes occurring at constant pressure.

Understanding these functions helps in analyzing how energy is exchanged and transformed in various thermodynamic processes.

Conservation of Energy

The principle of conservation of energy is a cornerstone in physics and is encapsulated in the first law of thermodynamics. This principle asserts that energy cannot be created or destroyed but only transformed from one form to another.
In practical terms, this means:

• The total energy of an isolated system remains constant.
• Energy can switch forms, like from potential to kinetic energy, or be transferred, such as from thermal energy into mechanical work.
• The equation \( \Delta U = Q - W \) showcases this conservation during processes where heat and work are the primary modes of energy transfer.

For students, this principle underscores a fundamental truth in physics, empowering them to understand various natural and engineered processes. By mastering the concept of energy conservation, you gain the ability to predict the outcome of energy exchanges in all sorts of systems.