 Welcome back. Now it is time to look at what in thermodynamics we call energy functions. We are used to one energy function and that is the thermal energy. Let us look at some properties of thermal energy. We will use the laws of thermodynamics. We know that our thermal energy u is defined using the first law of thermodynamics. Not an energy function but a related property s is defined using the second law of thermodynamics. We have a basic property relation which relates u and s. It is Tds is du plus pdv. And after this we have two laws which bring in interactions and the first law is in its differential form. Again remember we are looking at a closed system which is simple compressible and which is at rest. Hence, we will have dq equals du plus dw. And we will have the second law which says Tds is greater than or equal to dq. And if you substitute for dq from the first law we get Tds is greater than or equal to du plus dw. Notice that when we write a property relation Tds will be followed by an equality and on the right hand side we will have pdv. Whereas, when we write the second law, Tds will be followed by greater than or equal to and on the right hand side you will either have dq an interaction or a combination of du and dw where du is a differential of property. But dw is a small work interaction. Just the way we have u and the way we have defined in fact, we have started using enthalpy without really appreciating its use. Use will be appreciated only when we go to the study of open thermodynamic systems. And we have defined the enthalpy which is defined as u plus pv. Since it is related to u, if u is thermal energy this is known as the enthalpy and it is in general known as an energy function in thermodynamics. The first energy function is thermal energy. The second energy function which we have already defined is the enthalpy. And it is now time for us to define two more useful energy functions. And let us define them now. The third energy function which we will define is known as the Helmholtz function. This is given the symbol A usually. Earlier the symbol for some reason was F, but now A is the accepted symbol. This is defined as u minus Ts. This is the third energy function. And the fourth energy function which we will define and use is the Gibbs function. The symbol is G and it is defined as u plus pv minus Ts. And because u plus pv is enthalpy we can write it as H minus Ts or since u minus Ts is the Helmholtz function it is also equal to A plus pv. In a short while we will look at some peculiar properties of these functions. Thank you.