Why Isothermal Processes Cannot Occur in Isolated Systems

Understanding the behavior of systems in thermodynamics, particularly in the context of isolated systems, is crucial for many scientific and engineering applications. An isothermal process is a thermodynamic process where the temperature of the system remains constant. For this process to occur, heat must be exchanged with the surroundings to maintain the constant temperature, especially when work is being done on or by the system.

Isolated Systems and Their Characteristics

An isolated system is one that does not exchange any heat or matter with its surroundings. This means that any work done on or by the system will result in a change in internal energy, which in turn causes a change in temperature. Since an isothermal process requires a constant temperature, these conditions directly contradict each other, making an isothermal process impossible in an isolated system.

Key Principles Explained

No Heat Exchange

Isolated systems prevent any form of heat transfer. If a process is to be isothermal, it must maintain a constant temperature, which requires heat to be exchanged with the surroundings. In an isolated system, this exchange is not possible, leading to a temperature change and thus violating the isothermal condition.

Internal Energy Change

Work done on or by a system in an isolated environment changes its internal energy. This internal energy change is directly related to a temperature change. Since an isothermal process requires a constant temperature, any internal energy change that occurs due to work done will necessarily cause a temperature change, making such a process impossible in an isolated system.

Challenging the Common Understanding

The concept of isothermal and adiabatic processes can sometimes be misleading. While it is theoretically possible to perform an isothermal process by ensuring continuous heat exchange, the nature of isolated systems makes this impossible. For instance, the universe itself can be considered an isolated system, but the possibility of performing an isothermal process within the universe depends on the ability to facilitate heat transfer.

The Example of a Thermoflask

Imagine placing a system inside a thermoflask, which is itself an isolated system. If system A is defined within the thermoflask, it is still not an isolated system because the thermoflask itself is isolating the surroundings from system A. Therefore, the space containing system A is not an isolated system. This misunderstanding highlights why performing an isothermal process within an isolated system is fundamentally impossible.

Conclusion

For an isothermal process to occur, the system must be capable of exchanging heat with its surroundings. In an isolated system, such exchange is impossible, leading to inevitable changes in temperature when work is done. This understanding is crucial for distinguishing between different types of thermodynamic processes and the conditions under which they can be performed. The key takeaway is that isothermal processes can only occur in systems that are not isolated, highlighting the necessity of considering external factors in thermodynamic analysis.