Therefore, it may be necessary to construct more exact differential equations by building them up based on the actual system performance rather than a theoretical model.
12.
In other words, for a holonomic process function, \ lambda may be defined such that dY = \ lambda \ delta X is an exact differential.
13.
A simple but significant case is the-form of angle measure on the unit circle, written conventionally as ( described at closed and exact differential forms ).
14.
Likewise, with a well-defined pressure,, behind the moving boundary, the work differential,, and the pressure,, combine to form the exact differential
15.
To say that the expression given is a " representative " of the Chern class indicates that'class'here means up to addition of an exact differential form.
16.
So, in order for a differential " dQ ", that is a function of four variables to be an exact differential, there are six conditions to satisfy.
17.
It follows from the properties of an exact differential ( see equation 8 in the exact differential article ) and from the energy / entropy equation of state that, for a closed system:
18.
It follows from the properties of an exact differential ( see equation 8 in the exact differential article ) and from the energy / entropy equation of state that, for a closed system:
19.
Since the entropy is an exact differential, using the chain rule, the change in entropy when going from a reference state 0 to some other state with entropy may be written as where:
20.
An " exact differential " is sometimes also called a'total differential', or a'full differential', or, in the study of differential geometry, it is termed an exact form.
