conservation of energy

The first law of thermodynamics which is a statement of the conservation of energy principle states,

$$dQ~-~dW~ =~dE$$ (3.12)

$$=~{{dE} \over {dt}}$$ i.e.,

where dQ is the heat added to the system, dW is the work done by the system and dE is the consequent change in energy of the system.

In addition, we have

$$E_{system}~=~\int_{system}e~dm~=~\int_{system}e~\rho~d \forall$$ (3.13)

Energy, e is a sum of internal energy, u, kinetic energy and potential energy. Thus

$$e~=~u~+~{{V^2} \over 2}~+~gz$$ (3.14)

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney