State Functions are the functions that are independent of the path of the function i.e. they are concerned about the final state and not how the state is achieved. State Functions are most used in thermodynamics. In this article, we will learn the definition of state function, what are the state functions in Thermodynamics, and how they differ from path function.
What are State Functions?
State function is a property that only depends on the current state and not on the path taken to reach that state.
In other words, it doesn’t matter how you got there, just where you are. It provides valuable information about the state without requiring knowledge of the previous changes that led to the current state.
Examples of State Functions in Thermodynamics
State functions are crucial in thermodynamics as they provide a way to describe and analyze systems without having to consider the specific process that occurred. Here are some important state function examples commonly considered in thermodynamics:
Temperature (T)
Temperature is a measure of the average kinetic energy of the particles in a system. It is a state function because it describes the current state of the system, irrespective of the path taken to reach that state.
Pressure (P)
Pressure is the force applied per unit area on a surface. It is a state function as it only depends on the current state of the system. Pressure is an essential parameter to determine the behavior of gases and fluids in various thermodynamic processes.
Volume (V)
Volume refers to the amount of space occupied by a substance or system. In thermodynamics, volume is an essential parameter in determining the behaviors of gases and fluids, especially in processes involving expansion or compression.
Internal Energy(U)
Internal energy represents the total energy stored within a system, surrounding the kinetic and potential energies of its particles. Internal energy is crucial in understanding the energy transfers and changes within a system during various thermodynamic processes.
The Internal Energy is given by the following equation:
ΔU=Q-W
where ΔU represents the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Enthalpy(H)
Enthalpy is the total heat content of a system at constant pressure. It includes the internal energy of the system and the work required to move the system's surroundings.
Enthalpy is a state function as it depends only on the current state of the system, regardless of the path taken to achieve that state. It is particularly useful in studying heat transfer processes and chemical reactions.
The Enthalpy is given by the following equation:
ΔH = ΔU + PΔV
where ΔV represents the change in volume and P is the pressure.
Entropy(S)
Entropy is a measure of the disorder or haphazardness within a system. It is a state function as it depends only on the current state of the system, irrespective of the path taken to achieve that state.
Entropy provides valuable information about the direction and extent of spontaneous processes and is a fundamental concept in understanding thermodynamic equilibrium.
Gibbs Free Energy(G)
The Gibbs free energy, denoted by the symbol "G," predicts whether a chemical or physical process will occur spontaneously at constant temperature and pressure. It combines enthalpy, entropy, and temperature into a single equation. If the Gibbs free energy is negative, the process is spontaneous, indicating that the system tends to move towards a lower energy state.
Gibbs free energy is a state function as it depends only on the current state of the system, regardless of the path taken to achieve that state.
It is commonly used in chemical reactions and phase transitions to predict the possibility and direction of such processes.
The Gibb's Free Energy is given by the following equation:
ΔG = ΔH – TΔS
where ΔS refer to the change in entropy and T is the temperature.
Equation of State Function
State functions can be measured as integrals because integrals depend on only the function, its lower limit and upper limit. In the same way, state functions also depend on the property, its initial value and final value.
Consider a state function integral of enthalpy H, and t0 represents the initial state and t1 represents the final state is given by the following equation:
\int_{t_0}^{t_1} H(t)dt = H(t_1) - H(t_0)
This equation is similar to the equation of enthalpy:
ΔH = H final − H initial
Thus, the change in state function is the difference between its final value and initial value.
State Function Vs Path Function
The key differences between State Function and Path Function are given as follows:
|
|
A state function is a property that depends only the current state and not on the path taken to reach that state.
| A path function is a property that depends on the path taken to reach a particular state.
|
Different paths give the same value of the system.
| Different paths give different values of the system.
|
State function can be integrated using the initial and final values of the thermodynamic property of the system.
| Path function requires multiple integrals and limits of integration to integrate the property.
|
ΔU, ΔH, ΔS etc.
| δW , δQ etc.
|
Basically represented by equations or mathematical relations.
| Depends on the specific process or path.
|
Temperature, Pressure, Volume, Internal energy, enthalpy, entropy etc.
| Work, Heat and other energy transfer forms.
|
Read More,
State Function - Solved Examples
Problem 1: The entropy of a system increase from 69 j/k to 96 j/k during system process. Now find the entropy change for this process.
Solution:
Entropy change ( ΔS)=S final - S initial
ΔS= 96 - 69 j/k = 27 j/k
Problem 2: The initial internal energy of a system is 200 J, and the final internal energy is 350 J. Calculate the change in internal energy (ΔU) .
Solution:
Internal energy (ΔU) = Ufinal -Uinitial
ΔU=350J−200J=150J
Problem 3: Given that the enthalpy of a system changes from 450 kJ to 700 kJ during a certain process, Calculate the enthalpy change (ΔH) .
Solution:
Enthalpy (ΔH) = Hfinal -Hinitial
ΔH=700kJ−450kJ=250kJ
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