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# Isothermal Expansion of an Ideal Gas

## Expansion of an Isotherm

To understand the isothermal expansion of real gas and an ideal gas, it is necessary to first understand what both of these gases represent.
An ideal gas contains extremely elastic molecules and atoms. Because the molecules of an ideal gas travel faster than those of any other source, no intermolecular force of attraction exists between the elements. Furthermore, the molecules and atoms in an ideal gas are located relatively far away making contact impossible.
Perfect gases store heat in the form of kinetic energy inside each particle. This change in internal energy causes a change in temperature, resulting in exchange. Helium is a well-known example of an ideal gas. An ideal gas can convert its medium into a real gas under certain appropriate tolerance conditions.
Real gas is defined as a gaseous element with a low amount of intermolecular attraction interactions between its atoms and molecules. In the case of a perfect gas, it cannot survive and thrive in the natural environment. Real gases may work optimally in both high-temperature and low-pressure environments. Examples of genuine gases include nitrogen, helium, oxygen, and others.

## Define isothermal process

An isothermal process is described as a change in a specific system in which the temperature remains constant. Isothermal expansion results in T = 0 i.e. no change in the temperature. When a vacuum is extended, it causes a gas to expand freely. In the case of an ideal gas, the rate of free expansion is nil, implying that the work done is zero. The outcome is 0 regardless of whether the procedure is reversible or irreversible.
Some reversible situations of isothermal expansion include turning ice from its solid form to its liquid state as water, hydrogenation and dehydrogenation in chemical mills, and others. Work done against Joule's heating effect, friction, magnetic hysteresis, and other irreversible conditions are examples.

When a system has its internal energy changed, then it is given by the following condition:

âˆ†U = q + w --(1)

• âˆ†U = a shift in internal energy
• q = the heat provided by that particular system
• w = the precise quantity of work performed on the system

âˆ†U = q + pex âˆ†V

w = pex âˆ†V is the way used to describe work done in a vacuum situation. As a result, the upper equation can also be written as:

âˆ†U = q + pex âˆ†V

Moving on, if the volume in the condition is 0

âˆ†V = 0 â†’ âˆ†U = q + pex âˆ†V

U denotes the amount of work done in this NIL vacuum state. As a result, U = Q. 'qv' is used to represent that the volume, i.e. getting heat provided at a constant rate.

Consider another case in which an ideal gas, such as Helium, is subjected to isothermal expansion in the presence of vacuum (T = 0). In this case, the work done for this vacuum will be NIL, i.e. w = 0 since pex=0.

According to Joule's experiments, q =0, and so it is determined that work done is NIL, i.e. U = 0.
Finally, consider the following formula:

U = q + w.

With the points provided below, we can now formulate this assertion for both reversible and irreversible isothermal expansions processes:

• The isothermal reaction for a reversible change is denoted by the formula q = -w = pex (Vf-Vi).
• For an irreversible change, the isothermal reaction is given by q = -w = nRTln (Vf/Vi) = 2.303 nRT log (Vf/Vi).
• For example, in the instance of an Adiabatic change, it is expressed as Q = 0 and U = wad.

Remember that the work done in an isothermal expansion process for any given gas and vacuum condition is indicated by T = Constant, T = 0, and dT = 0.

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