Question

Internal energy is a state function. Explain.

Answer 1

We know that the thermodynamic properties which do not depend upon the path followed by the thermodynamic process are known as state properties. State property depends only upon the initial and final state of the system. The properties which depend upon the amount of matter are known as extensive properties.

Complete answer:
As we know, the thermodynamic system can be described by a number of thermodynamic parameters such as pressure, volume, temperature, internal energy, enthalpy etc. These can be divided into state functions and path functions. A state function is a property of a system whose value depends upon the initial and final states of the system. It is also known as point function. These types of functions describe an equilibrium state of a function and does not depend on how the system arrived in that state. For example, Internal energy is considered as a state function and is independent of the path followed to change the state of the system.
It is the total energy of a system. This is made up of a number of components such as translational kinetic energy of molecules, bond energy, electronic energy, intermolecular interaction energy of the constituents’ particles of the system etc. Internal energy is a function of pressure, volume, temperature etc. These all variables are state functions. Other examples of state function include mass, volume, pressure, temperature, density, entropy etc. There are some variables that depend upon the amount of matter present. These are known as Extensive properties. Examples include mass, volume etc. Some other variables are independent of the amount of matter known as intensive properties. Examples: density. Property of the system which depends upon only the state of the system and not on the path by which it is achieved is called state function. Internal energy does not depend on the path used to go from initial state to final state, but it depends on state. Internal energy of a system is an extensive property.

Note:
Remember that the thermodynamic properties which depend upon the path followed by the thermodynamic process are known as path properties. Internal energy only depends upon the initial and final state of the system, not on the path followed. So, the internal energy is a state function.