Search results
Results from the WOW.Com Content Network
More properly, one has ′ = where τ h is the translation operator, defined on functions by τ h φ(x) = φ(x + h), and on a distribution S by [] = []. In the theory of electromagnetism , the first derivative of the delta function represents a point magnetic dipole situated at the origin.
The definition of the Gibbs function is = + where H is the enthalpy defined by: = +. Taking differentials of each definition to find dH and dG, then using the fundamental thermodynamic relation (always true for reversible or irreversible processes): = where S is the entropy, V is volume, (minus sign due to reversibility, in which dU = 0: work other than pressure-volume may be done and is equal ...
This result seems to contradict the equation dF = −S dT − P dV, as keeping T and V constant seems to imply dF = 0, and hence F = constant. In reality there is no contradiction: In a simple one-component system, to which the validity of the equation d F = − S d T − P d V is restricted, no process can occur at constant T and V , since ...
The delta potential is the potential = (), where δ(x) is the Dirac delta function. It is called a delta potential well if λ is negative, and a delta potential barrier if λ is positive. The delta has been defined to occur at the origin for simplicity; a shift in the delta function's argument does not change any of the following results.
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure.
The inhomogeneous Helmholtz equation is the equation + = (),, where ƒ : R n → C is a function with compact support, and n = 1, 2, 3. This equation is very similar to the screened Poisson equation , and would be identical if the plus sign (in front of the k term) were switched to a minus sign.
Historically, the term 'free energy' has been used for either quantity. In physics, free energy most often refers to the Helmholtz free energy, denoted by A (or F), while in chemistry, free energy most often refers to the Gibbs free energy. The values of the two free energies are usually quite similar and the intended free energy function is ...
a A + d D → c C. In this case, K eq can be defined as ratio of B to C rather than the equilibrium constant. When B / C > 1, B is the favored product, and the data on the Van 't Hoff plot will be in the positive region. When B / C < 1, C is the favored product, and the data on the Van 't Hoff plot will be in the negative region.