a) | ![]() | Having studied physics and calculus, we recognize this as an exact differential, "differential kinetic energy" (dKE ) of the particle. The term is scalar, not vector. This term, an energy of the mass, a particle, is on the "system side" of the equation. |
b) | ![]() | This differential term, also exact (provided gravity (g) can be considered constant, which it can in many instances) integrates easily because the constant force of gravity is directed toward earth, i.e. in the negative K (-K) direction. Hence only the "Z" component of any displacement is non-zero. Some texts identify this term as "gravity work." (dWgravity). Though the term is on the "boundary" side of the equation, it greatly resembles a differential energy term, like kinetic energy. This becomes differential potential energy of the particle, (dPE). It will be moved to the left of the equality as will be explained shortly. |
c) | ![]() | Unlike Term 1) and 2), this term is not an exact differential. In thermodynamics, differentials of work are said to be "inexact" differentials. Calculus texts make no distinction, "inexact." |