Question

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

Short answer

The thermodynamic function associated only with the first law of thermodynamics is the Internal Energy \(E\).

Step-by-step solution

Understanding the Thermodynamic Functions

The functions mentioned are all important in thermodynamics. Entropy (S), is associated with the second law of thermodynamics and represents the disorder or randomness of a system. Internal Energy (E), comes from the first law and represents the total energy (kinetic plus potential) of the molecules in a system. Gibbs Free Energy (G) and Enthalpy (H), both are associated with energy changes at constant pressure, particularly useful for chemical reactions, and they embody concepts from both the first and second laws of thermodynamics.

Identify the Function Related to the First Law of Thermodynamics

Upon understanding the core associations of these thermodynamic functions, it becomes clear that the only function solely associated with the first law of thermodynamics, the law of conservation of energy, is the Internal Energy (E). The other functions, \(S, G,\) and \(H,\) are each associated with additional principles or laws beyond just the first law.

Key concepts

Entropy

Entropy, denoted by the symbol \(S\), is a fundamental concept in thermodynamics that measures the degree of disorder or randomness within a physical system. At its core, entropy provides a quantifiable measure of the number of specific ways a system can be arranged, often seen as a measure of uncertainty or the distribution of energy within a system.

The second law of thermodynamics states that in an isolated system, entropy will either increase or remain constant over time, never decreasing. This law implies that energy will naturally disperse and spread out to the point of equilibrium if not hindered or organized by external work.

For example, think about a room with two sections at different temperatures. Over time, the heat will distribute itself evenly throughout the room—an increase in entropy. Practically, the concept of entropy helps scientists and engineers understand processes like why heat moves from hot to cold, why certain chemical reactions occur spontaneously, and how to calculate the efficiency of heat engines.

Internal Energy

Internal Energy, represented by the symbol \(E\), is directly associated with the first law of thermodynamics, which is essentially the principle of conservation of energy. The internal energy of a system encompasses the total energy contained within—both kinetic and potential energy of all the particles in the system.

According to the first law, energy cannot be created or destroyed; it can be transferred from one system to another or converted from one form to another. This law allows for the calculation of energy changes in a system when it has work done on it or releases work, and when heat is added to it or removed from it. For instance, if a gas inside a container is heated, its internal energy increases as the molecules move faster and the distances between them become greater. If the gas is allowed to expand against an external pressure, it will do work on the surroundings and its internal energy will decrease accordingly.

Gibbs Free Energy

Gibbs Free Energy, denoted by \(G\), is a thermodynamic function that combines concepts from both the first and the second laws of thermodynamics. It is used to predict whether a process will occur spontaneously at constant pressure and temperature.

The Gibbs Free Energy is defined as \(G = H - TS\), where \(H\) is the enthalpy, \(T\) is the temperature, and \(S\) is the entropy of the system. The change in Gibbs Free Energy, \(\Delta G\), during a process is a crucial quantity. A negative \(\Delta G\) indicates that the process can occur spontaneously, while a positive \(\Delta G\) implies the process is nonspontaneous under the set conditions.

For example, when a chemist mixes certain reactants in a test tube, they can use the Gibbs Free Energy equation to determine if a reaction will take place without any external energy input, which is invaluable for the development of energy-efficient reactions in industrial applications.

Enthalpy

Enthalpy, represented by the symbol \(H\), is a thermodynamic quantity that reflects the total heat content of a system. It is related to both the first and second laws of thermodynamics and is particularly important in the context of chemical reactions and phase transitions taking place at constant pressure.

Enthalpy is defined as the internal energy of the system plus the product of the system's pressure and volume \(H = E + PV\). As such, when a system undergoes a chemical reaction at constant pressure, the change in enthalpy \(\Delta H\) corresponds to the heat absorbed or released by the system.

An important application of enthalpy is in the field of calorimetry, where the enthalpy change associated with chemical reactions, such as combustion, can be measured. This information is crucial for a wide variety of applications, from designing energy sources and materials to understanding biological metabolism.