' fundamental relations are important to thermodynamics. Their focus isn't on heat transfer
processes, instead they look at the states of matter in a system. In brief Gibbs' fundamental relations describe the entropy of a system as a function of it's extensive variables.
The first law of thermodynamics can be expressed mathematically.
dU = dQ + dW
Where U represents energy, Q represents heat
, and W represents work
had also expressed the law for fluids in terms of temperature
(V), and entropy
dU = T•dS - P•dV
The solution to the above equation is U = U(S,V)
. The limitation is that the amount of matter interint a system must be fixed for this relation. It can be avoided if the matter entering the system is treated as a thermodynamic variable
Gibbs' fundamental relations for simple systems
which can be derived from the above are as follows:
Gibbs' fundamental relation (entropy representation)
S = S(U, V, N1, N2, ... Nr)
Gibbs' fundamental relation (energy representation)
U = U(S, V, N1, N2, ... Nr)
Those two equations are considered the fundamental relations of thermodynamics. Where Ni, from i = 1 to r, are the chemical components of the system in moles.
The first law can be rewritten to be:
dU = (∂U/∂S)|V,N1... dS + (∂U/∂V)|S,N1... dV
The second law
, and zeroth law
can be described by the principles of least energy
, and maximum entropy
The third law states that as temperature approaches zero, the entropy of the system approaches zero. This puts a boundary condition
on any function of state regarding the function for entropy.