What is internal energy ? & how is internal energy of a real gas differs from that of ideal gas?

Ideal gases

An ideal gas is one which follows the ideal gas equation of state, namely

PV = (m/M) (MR) T = n Ru T

The universal gas constant has a value of 8.314 J/mol K or kJ/kmol K and is related to the specific gas constant by the relation Ru = (R /M)

The internal energy of an ideal gas is a function of temperature only and is independent of pressure and volume. That is,

u= u(T)

(∂u/∂P)T =0, (∂u /∂v)T = 0

Real gases:

The ideal gas law is only an approximation to the actual behavior of gases.

At high densities, that is at high pressures and low temperatures, the behavior of actual or real gases deviate from that predicted by the ideal gas law. In general, at sufficiently low pressures or at low densities all gases behave like ideal gases.

Hope this helps.

Thanks Awesome, but it a little more complicated.

What is internal energy, and how does that differ in ideal and real gases?

Internal energy is the sum of all the energys in the particles. In ideal gases, it exists as Kinetic energy only, there are no potential energies to consider. In real gases, there are attractions between molecules, so we have rotational energy, and vibration energy, as well as kinetic energy. In those molecules which are vibrating, and rotating, consider it like little springs, which have potential enrgy and moving energy oscillating.
That may be a function of temperature we measure, but it is not the same as what we consider in single moving particles, it is more complicated, and we have to use statistical approaches in deriving relationships. those vibrational and rotational motions may be a function of density (particle proxmity) also, which is altered by pressure, In an idealized gas, this is not so.

Internal energy is the total energy contained within a substance. It includes the kinetic energy of the particles (due to their movement) and the potential energy between the particles (due to their interactions). Internal energy is denoted by the symbol U.

Now, let's discuss how the internal energy of a real gas differs from that of an ideal gas.

In an ideal gas, the particles are assumed to have no volume and there are no intermolecular forces present. This means that the potential energy due to interactions between particles is considered to be zero. The internal energy of an ideal gas depends solely on the kinetic energy of the particles and is directly proportional to the temperature. The mathematical expression for the internal energy of an ideal gas is U = (3/2) * n * R * T, where n is the number of moles of gas, R is the gas constant, and T is the temperature.

On the other hand, in a real gas, the particles have volume and experience intermolecular forces. This means that the potential energy due to particle-particle interactions becomes significant. The internal energy of a real gas depends not only on the kinetic energy of the particles but also on the potential energy due to intermolecular forces. The presence of these forces leads to deviations in the behavior of real gases from that of ideal gases.

Therefore, the internal energy of a real gas is influenced by factors such as pressure, volume, temperature, and the nature of intermolecular forces. The mathematical expression for the internal energy of a real gas is complex and depends on the specific properties of the gas. It cannot be expressed in a simple formula like that of an ideal gas.