Fundamental Equation Mathematics & Economics Math Problem (Math Problem Sample)

Fundamental Equations in Differential Forms
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Fundamental Equations in Differential Forms
Fundamental equations are simple but important equations derived from the definition of entropy and the First Law of thermodynamics. The derived equations can be expanded to form complex thermodynamic functions using various mathematical manipulations. The equations, U, H, A and G are dependent and corresponds to small changes of states of reactions. Fundamental equations explain more states of chemical reactions and changes that happen when any factor affecting certain equilibrium is affected. In general, the four fundamental equations demonstrate how different factors, which can be controlled measured experimentally influence the four basic thermodynamic quantities.
Fundamental equations (also known as fundamental thermodynamic equations) can be presented in their differential form to describe Helmholtz energy, internal energy, Gibbs energy, and enthalpy in their natural variables. All the four equations are derived from the First Law of thermodynamics presented in its differential form in Equation 1 below.
Equation SEQ Equation \* ARABIC 1: First Law of Thermodynamics Equation
dU=ðq+ðω
Where:
U=internal energy system,
ω=work of the system, and
q=heat flow of the system.
While other scholars (Moran et al., 2010; Lemmon & Span, 2006) use the normal differential symbol, d, Olver, (2012) used the symbol ð to represent inexact differentials, indicating that both ω and q are path functions. In other words, the state functions, U, indicates that internal energy is a result of work done and heat flow.
The work done, ω, is assumed to be only from Pressure-Volume (PV) work. That is