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Isothermal Expansion
In an ideal gas, all the collisions between molecules or atoms are perfectly elastic and no intermolecular force of attraction exists in an ideal gas because the molecules of an ideal gas move so fast, and they are so far away from each other that they do not interact at all. In the case of real gas, they have negligible intermolecular attractive forces. Ideal gas does not exist naturally. However, gases behave most ideally at high temperature and low-pressure conditions. The entire internal energy in an ideal gas is in the form of kinetic energy of the particles and any change in the internal energy results in a change of temperature.
Now that we have a basic understanding of the concept of an ideal gas let us see what the meaning of an isothermal expansion is and what is an isothermal process. An isothermal process is a change in the system such that the temperature remains constant. In other words, in an isothermal process ∆T = 0.
Isothermal Expansion
Free expansion of a gas occurs when it is subjected to expansion in a vacuum (pex=0). During free expansion of an ideal gas, the work done is 0 be it a reversible or irreversible process.
It is known that the change in internal energy of a system is given as:
∆U = q + w —(1)
Where ∆U represents the change in internal energy, q is the heat given by the system and w is the work done on the system.
Depending upon the type of process the above equation can be written in different ways.
The work done in vacuum, w = pex∆V. Therefore, equation 1 can be given as:
∆U = q + pex∆V
If this process is done at constant volume then ∆V = 0. Thus,
∆U = Q
qv implies that the heat is supplied at a constant volume.
When an ideal gas is subjected to isothermal expansion (∆T = 0) in vacuum the work done w = 0 as pex=0. As determined by Joule experimentally q =0, thus ∆U = 0.
For isothermal reversible and irreversible changes; equation 1 can be expressed as:
Isothermal reversible change: q = -w = pex(Vf-Vi)
Isothermal reversible change: q = -w = nRTln (Vf /Vi) = 2.303 nRT log (Vf /Vi)
Adiabatic change: q =0, ∆U = wad
Because heat engines may go through a complex sequence of steps, a simplified model is often used to illustrate the principles of thermodynamics. In particular, consider a gas that expands and contracts within a cylinder with a movable piston under a prescribed set of conditions. There are two particularly important sets of conditions. One condition, known as an isothermal expansion, involves keeping the gas at a constant temperature. As the gas does work against the restraining force of the piston, it must absorb heat in order to conserve energy. Otherwise, it would cool as it expands (or conversely heat as it is compressed). This is an example of a process in which the heat absorbed is converted entirely into work with 100 percent efficiency. The process does not violate fundamental limitations on efficiency, however, because a single expansion by itself is not a cyclic process.
The second condition, known as an adiabatic expansion (from the Greek adiabatos, meaning “impassable”), is one in which the cylinder is assumed to be perfectly insulated so that no heat can flow into or out of the cylinder. In this case the gas cools as it expands, because, by the first law, the work done against the restraining force on the piston can only come from the internal energy of the gas. Thus, the change in the internal energy of the gas must be ΔU = −W, as manifested by a decrease in its temperature. The gas cools, even though there is no heat flow, because it is doing work at the expense of its own internal energy. The exact amount of cooling can be calculated from the heat capacity of the gas
Conclusion
Thus we conclude that One condition, known as an isothermal expansion, involves keeping the gas at a constant temperature. As the gas does work against the restraining force of the piston, it must absorb heat in order to conserve energy. Otherwise, it would cool as it expands (or conversely heat as it is compressed).
