Energy And The 1st Law of Thermodynamics Explanation and Proofs

In the view of fact that thermodynamics is a study of energy and it's transformation, it not surprising that a large portion of the subject matter of thermodynamics deals with the study of energy. Accordingly, it is imperative that we identify and discuss certain forms of energy which are essential for a proper understanding of the subject as a whole. In this article, five main forms of energy, namely; internal energy, potential energy, kinetic energy, heat and work will be discussed while other forms which produce significant changes during thermodynamics will be introduced later in the contents.

INTERNAL ENERGY 

Internal Energy, normally denoted by symbol U, is the energy stored in a system as a result of continuous internal motion of its molecules. We can not arrive at an absolute value of internal energy, however, since temperature as discussed is a manifestation of the degree of molecular activity within a system, we can increase or decrease the magnitude of the internal energy of a system by raising or lowering it's temperature.
Internal energy is a property, although it's value cannot be directly measured, it can be related to changes in other measurable properties such as temperature, specific volume and pressure. The unit of the specific internal energy is joules per kilogram (J/Kg). However, for a mass m of the system, the total internal energy U is given by;
               U = mu

POTENTIAL ENERGY AND KINETIC ENERGY. 

potential Energy is the energy possessed by virtue of its position relative to some reference level. The potential energy P.E of a body of mass m, in a gravitational field with acceleration of gravity g, at some height Z above a reference level is expressed by;
           P.E = mgz
The potential energy expressed above is an extensive property, The corresponding intensive property, that is, the potential energy per mass is defined thus;
         P.E = gz
The kinetic energy K.E of a body is the energy it possess as a result of its motion and is given by;
        K.E = ½mC²
Where m is the mass of the body and C is the velocity of its motion. The kinetic energy per unit mass, an intensive property is then expressed by;
         k.E = ½C²