Mathematical Approach to Thermodynamical System

Abstract

The present paper reports the new energy equation (TdS equation) for thermodynamic system using mathematical formulation. New TdS formula contains C p (specific heat at constant pressure) and Cv (specific heat at constant volume). We have also discussed about the change in internal energy with respect to pressure and it will be treated for ideal gas as well as real gases. The internal energy of a system can be understood by examining the simplest possible system: an ideal gas. Because the particles in an ideal gas do not interact, this system has no potential energy. The internal energy of an ideal gas is therefore the sum of the kinetic energies of the particles in the gas. The internal energy of systems that is more complex than an ideal gas can’t be measured directly. In the present work we have observed that the internal energy of the system depend upon pressure developed in. We can therefore monitor changes in the internal energy of a system by watching what happens to the pressure of the system. We can conclude that the change in the internal energy of a system with respect to pressure at constant is inversely proportional to volume elastic constant (E).