Thermodynamics is a science which is built upon experimental facts that cannot be proven. But no one has so far succeeded to refute these principles. There are two experimental facts upon which thermodynamics is built. These are: the law of conservation of energy upon which the first law of thermodynamics is built.
The second experimental fact is that heat cannot be transferred from a cold reservoir to a hot reservoir without the expenditure of work. This second fact is also a taken for granted reality that cannot be proven. Thermodynamics can tell us if a chemical process will take place or not. In addition, it can tell us if a chemical process will take place spontaneously or not.
The thermodynamic functions that tell us about these facts are called the enthalpy and the free energy of Gibbs. The thermodynamic function that tells us if a process is spontaneous or not is the free energy of Gibbs which is symbolized as G. It is so named for its discoverer Williard Gibbs.
For negative values of G the chemical process is considered spontaneous. For positive value of G the process is not spontaneous. At G =0 the process is said to be in equilibrium. The thermodynamic function G is a basic function of thermodynamic systems under the control of pressure and temperature and number of moles.
The thermodynamic function which will tell us if a process will take place or not is called the enthalpy function which is symbolized as H. Negative value of H tell us that the chemical process is exothermic and the whole process will proceed favorably. Positive value of H tells us that the process is endothermic with unlikelihood that the process will take place.
The enthalpy is a basic function of thermodynamics which like the free energy of Gibbs depends on the pressure with the difference that instead of the temperature it is dependent on its conjugate extensive variable the entropy. The enthalpy is equal to the heat of the system under constant pressure
The first law of thermodynamics is actually the conservation of energy law which states that the internal energy of a given system or E is equal to its heat plus the work done on it. in formula:
E = Q + W
where Q is the heat of the system and W is the work done on it.
In an expansion process of a gas against vaccum there is no thermal effect or a change in temperature. This is an experimental fact that was observed by Joule in one experiment. As a result there is no change in energy as a function of volume and pressure. This is true for an ideal gas.
For non-ideal gases the change in energy as a function of volume and pressure is not zero. These results can be obtained by writing the exact differential of the energy extensive function as a function of volume and temperature.
The heat capacity of a given system is defined as the change in in the heat of a system as a function of temperature. There are two types of specific heats. These are: volume independent specific heat or Cv and pressure independent specific heat or Cp.
For an ideal gas, the energy of a given gas is given by
E = CvdT
This states that the energy of an ideal gas is equal to the specific heat at constant volume times the change in temperature. The relation between Cv and Cp can be obtained easily for an ideal gas. It is given by the following equation
Cp – Cv = nR
