Helmholtz Free Energy and Gibbs Free Energy, definition and its derivation detailed explanation are given here.
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Helmholtz Free Energy (Work Function)
- Helmholtz Free Energy is also known as Work Function.
- It is denoted by, \(A.\)
- It can be defined as \[A=U-TS ------------ (1)\]
- All the properties \(U, T \)and\( S\), which define Helmholtz free energy, are the state functions; therefore, Helmholtz free energy is also a state function.
- Properties \(U\) and \(S\) are extensive properties, therefore Helmholtz's free energy is also an extensive property.
- Let's consider an isothermal (temperature constant) reversible process.
- The process occurs from state 1 to state 2.
- In this process, change in Helmholtz free energy can be written as, \[\Delta A = \Delta U - T\Delta S ----------- (2)\]
- For the reversible process, heat absorbed by the system is given by \[Q_R = T\Delta S\]
- Put this value in equation no. (2) \[\Delta A = \Delta U - Q_R ----------- (3)\]
- The first law of thermodynamics for closed system says, \[\Delta U = Q - W ------------ (4)\]
- Put the value of \(\Delta U\) from equation no (4) to equation no (3) \[\Delta A = \cancel{Q} - W - \cancel{Q_R}\]
- The above equation shows the decrease in the work function for the reversible isothermal process.
- As we know, reversible work is the maximum work done by any of the processes.
- So here we can also say that maximum available work in an isothermal process is \(-\Delta A.\)
Where,
\(U=\) Internal Energy of the system,
\(T=\) Temperature of the system,
\(S=\) Entropy of the system.
There is no change in T because the process is isothermal.
Rearranging the equation
\[W_R = - \Delta A --------------- (5)\]Gibbs Free Energy
- It is denoted by, \(G.\)
- It can be defined as \[G=H-TS ------------ (6)\]
- Gibbs's free energy is also an extensive property.
- Gibbs's free energy is useful in the study of phase equilibria and chemical reaction equilibrium.
- As per the definition of enthalpy, $$H=U+PV$$
- Put this value of \(H\) in equation no (6) $$G=U+PV-TS$$
- From equation (1), we can write, $$G=A+PV-----------(7)$$
- Let's take a reversible process at constant pressure and temperature.
- Changes take place in the process from state 1 to state 2.
- Gibbs free energy change can be given by, $$\Delta G=\Delta A+\Delta (PV)-----------(8)$$
- From the equation of work function, we know \(\Delta A = - W_R,\) for reversible isothermal process, and \((\Delta PV)\) can be written as \(P \Delta V\) for the constant pressure process. $$\Delta G=- W_R+P\Delta V$$
- \(P\Delta V\) represents expansion work
- \(W_R\) represents total work (expansion work plus other work)
- So, here Gibbs free energy represents maximum work available other than expansion work.
- So maximum 'net work' represented by \(W_R^{'}\) can be given by, \[W^{'}_R =-\Delta G\]
- Here we can conclude that the change in Gibbs free energy gives the value of net useful work; it does not include the energy utilized in expansion work.
- So that is why it is called free energy.
Rearranging this equation,
$$-\Delta G=W_R-P\Delta V$$Here,
What is Chemical Engineering | About scope for chemical engineering
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Newtonian and Non-Newtonian Fluids
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