Question

Among the following, the state function(s) is(are) (A) Internal energy (B) Irreversible expansion work (C) Reversible expansion work (D) Molar enthalpy

Short answer

The state functions among the options are (A) Internal Energy and (D) Molar Enthalpy.

Step-by-step solution

Understanding State Functions

State functions are properties whose values depend only on the state of the system, not on the path or process by which the system arrived at its state. Common examples include internal energy, enthalpy, entropy, and Gibbs free energy.

Identifying State Functions Among the Given Options

Option (A) Internal Energy is a state function as it depends only on the initial and final states of a system, not on how the energy change was enacted. Option (D) Molar Enthalpy is also a state function as it is a measure of heat content and only depends on the current state of the system.

Eliminating Non-State Functions

Option (B) Irreversible expansion work and Option (C) Reversible expansion work are not state functions. This is because work is a path function; it depends on the specific process by which the system changes from one state to another.

Key concepts

Understanding Internal Energy

Internal energy, denoted as U, is a key concept in thermodynamics and represents the total energy contained within a system. This energy includes both the kinetic energy of the system's particles and the potential energy of the interactions between them.

As a state function, internal energy is independent of how the system reached its current state. In other words, no matter what path or process a system undergoes, if it starts and ends in the same state, the internal energy will be the same. Mathematical changes in internal energy are represented by the equation \(\Delta U = Q - W\), 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.

To further clarify, imagine heating a pot of water. Whether the heat is applied quickly or slowly, the increase in the water's internal energy, once reaching a certain temperature, remains constant.

Molar Enthalpy and its Significance

Molar enthalpy, usually symbolized by \(H\), is the enthalpy or heat content per mole of a substance. The term is particularly useful when dealing with chemical reactions and phase changes. Enthalpy combines the system's internal energy with the product of its pressure and volume: \(H = U + PV\).

Being a state function means that molar enthalpy depends only on the current state of the system, not on how that state was achieved. For example, when water boils at standard atmospheric pressure, the molar enthalpy of vaporization is always the same, irrespective of the heating method used.

Practical Application

Consider the case of a chemical reaction running in a calorimeter. The molar enthalpy change associated with the reaction tells us how much heat is absorbed or released per mole of reactant, crucial information for understanding reaction energetics.

Irreversible Expansion Work

Work is a measure of energy transfer when a force moves an object, and in thermodynamics, it often refers to the work done by or on a system as it expands or compresses. Irreversible expansion work occurs when a system changes volume against an external pressure in a manner that cannot be exactly retraced in reverse.

Since the exact path taken by the system affects the amount of work done, this makes irreversible expansion work a path function, not a state function. For example, when gas expands rapidly into a vacuum, there’s no resistance, and hence no work is done by the gas, illustrating the dependence on the specific expansion path.

Contrasting with Reversibility

Unlike reversible processes, which can be conducted infinitely slowly so that the system is always in equilibrium, irreversible processes often involve dissipating energy into the surroundings, further indicating its path dependence.

Reversible Expansion Work

Reversible expansion work represents the ideal maximum work that can be done by a system on its surroundings as it expands. Reversibility refers to conducting a process such that the system and its surroundings can be returned to their initial states without any net changes.

The concept of reversible work is a theoretical construct used for analyzing systems and understanding the limits of efficiency. In a reversible expansion, the process occurs infinitely slowly and the system remains in near-equilibrium with its surroundings throughout the process. Mathematically, reversible work in an isothermal expansion of an ideal gas is expressed as \(W_{rev} = -nRT \ln(\frac{V_f}{V_i})\), where \(n\) is the number of moles, \(R\) is the ideal gas constant, \(T\) is the temperature, and \(V_i\) and \(V_f\) are the initial and final volumes, respectively.

Even though reversible processes are idealizations and cannot be achieved in reality, they are vital for calculating a system's maximum possible efficiency and for formulating fundamental thermodynamic laws like the second law of thermodynamics.