What is the mathematical expression for the first law of thermodynamics?

Answer 1

Partial molar gibbs free energy is actually a derivative or infinitesimal change in molar gibbs free energy wrt an infinitesimal change in mols of that particular component it is also known as the chemical potential (greek letter mu). This is not particularly applicable/useful for pure components but when dealing with mixtures and chemical reactions it can be so it is often given a subscript denoting the species/component it is referring to. Initially many people would not believe it to be any different than the molar gibbs free energy but it is mainly due to two things 1) Entropic effects and 2) Structural and or Chemical non-idealities. So in effect partial molar gibbs free energy is equal to the following expression: (Molar Gibbs free energy)+(Entropic contribution)+(Chemical non-ideality). Molar Gibbs free energy is for a pure component and i will denote it G. Entropic contribution can be derived from further study of thermodynamics is the Universal Gas Constant (R) times the Temperature in Kelvin (T) times the natural logarithm of the mol fraction (ln(x)). Chemical non-ideality is generally given the term excess gibbs free energy (GEX) which has to do with the way in which molecules of the various components interact for instance non-polar molecules with polar molecules and it is modeled in many different ways some of which have advantages over others and studying more advanced thermodynamics will give one more insight into this. The overall expression thus becomes G+RT(ln(x))+GEX.

Answer 2

delta G= delta H - TdeltaS

∆G = ∆H - T∆S

where ∆G is is the change in Gibb's free energy

∆H is the change in enthalpy

∆S is the change in entropy

T is the temperature in KelvinThe mathematical expression for the change in free energy of a system delta G=delta H-T deltas. The answer is delta G is the change in free energy.

Answer 3

For a closed

system:

ΔE =

Q + W

OR
ΔE =

Q + ⌠PdV

where

ΔE is the increment of energy of the system, Q is the energy received by the

system as heat, W is the energy received by the system as work, and ⌠PdV

is the

work done by the surroundings over the system by compression of the system.

Note that dV

is the variation of volume of the surroundings and is equal to the

variation of the system but with opposite sign. dV

sur

=

- dV

syst

.

Answer 4

If we represent the change in energy by the symbol Δe , then the formula is:

Δe = (Ef - Ei)

where

Ef = final energy

Ei = initial energy

Note that Δe can be positive, negative, or zero, corresponding to processes in which

the energy of the system increases, decreases, or is constant, respectively.

Answer 5

δG = δH + TδS at constant temperature

Legend: δ = 'delta' = difference in to gibbs energy levels