Internal energy formula physics and examples

“The sum of all forms of molecular energies (kinetic and potential ) of a substance is termed as its internal energy.”In the study of thermodynamics,usually ideal gas is considered as a working substance. the molecules of an ideal gas are mere mass points which exert no force on one another. so the internal energy of an ideal gas system is generally the transnational kinetic energy of its molecules. since, the temperature of a system is defined as the average kinetic energy of its molecules, thus for an ideal gas system, the internal energy is directly proportional to its temperature.

when we heat a substance energy associated with its atoms or molecules is increase i.e , heat is converted to internal energy.

It is important to note that energy can be added to a system even though no heat transfer take place. for example, when two objects are rubbed together, their internal energy increases because of mechanical work. the increase in temperature of the object is an indication of increase in the internal energy. similarly, when an object slides over any surface and comes to rest because of frictional force, the mechanical work done on or by the system is partially converted into internal energy.

In thermodynamics, internal energy is a function of state. consequently, it doesn’t depends on path but depends on initial and final states of the system. consider a system which undergoes a pressure and volume change from Pa and Va to Pb and Vb respectively, regardless of the process by which the system changes from initial to final state. by experiment it has been seen that the change in internal energy is always the same and is independent of paths C1 and C2.internal energy

Thus internal energy is similar to the gravitational potential energy. so like the potential energy, it is the change in internal energy and not its absolute value, which is important.

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