[Physics Class Notes] on Difference Between Isothermal and Adiabatic Process Pdf for Exam

Thermodynamics deals with the two most important concepts of thermal physics, i.e., isothermal and adiabatic processes. The adiabatic process is the one that deals with the transfer of energy between the system and surroundings in the form of work. In an adiabatic process, there is no transfer of any heat or mass between the system and the surroundings. The main concept behind the difference between adiabatic and isothermal processes is that while the former is isolated from the surroundings, the latter is not.

Isothermal Process

Unlike adiabatic processes, the isothermal process is the one in which there is heat transfer between the system and the surroundings and the temperature of the system remains constant throughout the process. The temperature is kept constant by the transfer of heat between the system and the surroundings. The name itself explains that the temperature remains the same.

It is also interesting to note that in certain cases, the process is isothermal and adiabatic at the same time. This is especially true in cases of irreversible processes. Joule-Thompson expansion and also the free expansion of ideal gases are the best example of such a system involving both processes at the same time. A very simple way to explain this is deduced below.

The isothermal process is the thermodynamic process in which there is no change in the temperature throughout the process, i.e., ΔT = 0. This can only be maintained with the transfer of heat in between the system and the surrounding. This condition hence is used to distinguish between the isothermal and adiabatic processes. For the heat transfer to take place, the system should be surrounded by a thermal reservoir. The thermodynamic changes that take place inside the system are slow enough for maintaining and adjusting a constant temperature of the system via the heat exchange with the surrounding.

From the above explanation, it is clear that isothermal processes can occur in any kind of system that has some way of recovering the lost heat and regulating the temperature, be it highly structured machines or any of the living cells, which is also a significant factor to distinguish between the isothermal and adiabatic processes. The most famous and best example of a machine carrying out isothermal processes is the Carnot Cycle. Usually, when studying the chemical reactions, thermodynamically speaking, first, the effects under isothermal conditions are analyzed before moving on to analyze the temperature effect on the process. Other examples of isothermal processes are phase changes, such as melting or evaporation, where they also occur at constant pressure. To understand non-isothermal processes, it is a general practice to solve the same process under isothermal conditions and then understand the changes in the non-isothermal processes.

Isothermal processes are an interesting choice when it comes to the study of ideal gases. Since there are no intermolecular forces in ideal gases, the internal energy of the ideal gases in an isothermal process remains constant. Also, according to Joules’ second law, the internal energy of a fixed amount of an ideal gas depends on the temperature only. Hence, with no change in temperature, the internal energy of the isothermal process also remains constant. But this is only true for the ideal gases. For liquids, solids, and real gases, the internal energy of the system depends on the temperature as well as on pressure.

To decrease the volume and increase the pressure of a system in isothermal compression, significant work needs to be done. When work is done on the gas, it increases the internal energy and, in turn, increases the temperature. For the maintenance of the temperature, energy must leave the system as heat into the surroundings. In the case of an ideal gas, the amount of energy leaving the system is equal to the work done on the system; as already mentioned above, the internal energy does not change. When there is isothermal expansion, the energy given to the system does the work on the surrounding. With suitable help, the change in the gas volume can perform useful mechanical work as well.

The difference between isothermal and adiabatic processes is that for an adiabatic process, there is no heat flow in and out of the system as the system is well insulated. Hence, ΔQ = 0. And if there is no work done, there is no change in the internal energy. Hence, such a process also becomes isothermal. Thus, under certain conditions to specify a unique process, it is not sufficient to mention that the process is isothermal. It becomes necessary depending on the parameters to tell whether it is adiabatic as well.

Adiabatic Process

As mentioned in the introduction, to differentiate between isothermal and adiabatic processes thermodynamically, the adiabatic process is a thermodynamic process in which there is no transfer of heat or mass in between the system and the surroundings. As per the difference between the isothermal and adiabatic processes, in an adiabatic process, the energy is transferred only in the form of work done. Because of the difference between isothermal and adiabatic, the adiabatic process is a key process also as the theory conceptually supports the explanation of the first law of thermodynamics. 

As per the definition and the isothermal and adiabatic process difference, an adiabatic system in which there is no transfer of heat and no change in the heat of the system is said to be adiabatically isolated. The assumption of an adiabatic process is for simplifying the processes and understanding them. Once the assumption is made and the process simplified, it makes the calculations easier. For example, the compression of gas inside the cylinder of an engine is assumed to occur very rapidly on the time scale of the compression process; some of the system’s energy can be transferred out in the form of heat to the surroundings. Although the cylinders are not insulated and are quite conducive, the process is idealized as adiabatic. The same can be said for the expansion process of such a system.

Isothermal and Adiabatic Process at the Same time

From the First Law of thermodynamics, we know

ΔU = ΔQ-ΔW, where W is work done, Q is heat energy, and U is internal energy

Now, in an adiabatic process, [ Delta Q = 0], 

I.e.,  [ Delta U = 0 – W = -W],

Now, for an ideal gas, we know that [ Delta U = C_{v} * Delta T ]

Isothermal process means T = 0 

Now, substituting this, we get

[ Delta U = 0], which means W= 0 from the above equation. 

This is therefore both isothermal as well as adiabatic.

Work done in an Adiabatic reversible compression is given as

[Delta W = n C_{V} Delta T]

Work done in an Isothermal reversible expansion is given as

[ W = -2.303~nRT~log~frac{P_{1}}{P_{2}}]

[ W = -2.303~nRT~log~frac{V_{1}}{V_{2}}]

The main difference between adiabatic and isothermal processes is that in the former, there can be no addition or release of heat to the system, resulting in a change of temperature of the system, while in the latter, heat can be added or released to the system in a way to keep the overall temperature constant.

Difference between Isothermal and Adiabatic Process

In order to differentiate between isothermal and adiabatic processes, the major difference betw
een isothermal and adiabatic processes, as clear from the introduction, is in the matter of heat transfer in between the surrounding and the system. The heat change by heat transfer is used to distinguish between isothermal and adiabatic processes as in the isothermal process; heat transfer occurs to maintain a constant temperature, while there is no such heat transfer in between the system and the surrounding. Some of the more significant differences between the isothermal and adiabatic process in tabular form are given below as a means to compare between isothermal and adiabatic processes:

Differences between Isothermal Process and Adiabatic Process