Thermodynamics is the branch of physics that explores the relationship between heat, work, temperature, and energy. Scientists study how systems interact with their surroundings by observing changes in certain measurable properties. These changes are described through specific thermodynamic processes that hold one of these properties constant to simplify analysis. The isothermal process is one such transformation, defined by maintaining a fixed temperature throughout the entire change.
The Core Definition of Constant Temperature
An isothermal process is defined as any physical or chemical change that occurs while the system’s temperature (\(T\)) remains unchanged. This means that the total change in temperature, \(\Delta T\), is zero from the initial to the final state.
When considering an ideal gas, the constant temperature condition has a direct consequence described by the Ideal Gas Law, \(PV=nRT\). Since the number of moles (\(n\)) and the gas constant (\(R\)) are fixed values, a constant temperature (\(T\)) forces the product of pressure (\(P\)) and volume (\(V\)) to remain constant as well. This relationship means that pressure and volume are inversely proportional during an isothermal change.
A distinguishing feature of this process for an ideal gas is that the internal energy (\(\Delta U\)) of the system remains zero. Internal energy for an ideal gas is dependent only on its temperature, reflecting the total kinetic energy of its molecules.
The Relationship Between Heat and Work
The conservation of energy in thermodynamics is governed by the First Law, which states that the change in a system’s internal energy (\(\Delta U\)) is equal to the heat (\(Q\)) added to the system minus the work (\(W\)) done by the system (\(\Delta U = Q – W\)). Since the change in internal energy (\(\Delta U\)) is zero, the equation simplifies to \(Q=W\).
This equality means that any heat energy added to the system must be completely converted into work done by the system, and vice versa. For instance, if a gas expands isothermally, it performs work on its surroundings, which would naturally cause a drop in its temperature. To prevent this cooling and maintain the constant temperature, an equal amount of heat must be continuously absorbed from the environment.
Conversely, if the gas is compressed, work is being done on the system, which would cause the temperature to rise. To keep the process isothermal, the system must release an equal amount of heat back into the surroundings.
Practical Requirements for Achieving the Process
Achieving a perfectly isothermal process is an idealized concept, but it can be closely approximated in real-world conditions. The first requirement is that the process must occur extremely slowly, a condition known as quasi-static. This slow pace is necessary to allow sufficient time for heat to transfer between the system and its surroundings, ensuring the temperature gradient remains virtually nonexistent throughout the change.
The second requirement is that the system must be in continuous thermal contact with a heat reservoir. This reservoir is a surrounding environment, such as a large water bath or the atmosphere, that is so massive its own temperature remains constant even after absorbing or supplying large amounts of heat. This large, stable environment acts as a thermal buffer, readily supplying or absorbing the exact quantity of heat required to offset the work being performed and keep the system’s temperature fixed.
A common real-world example of an isothermal process is the phase change of a substance, such as water boiling. When water boils at standard atmospheric pressure, its temperature remains fixed at \(100^{\circ}\) Celsius, even as heat is continuously added.
Distinguishing Isothermal from Other Processes
The uniqueness of the isothermal process becomes clearer when contrasted with the three other common thermodynamic processes. The isothermal process is defined by its constant temperature (\(T\)).
In contrast, the adiabatic process is defined by having no heat transfer (\(Q=0\)) into or out of the system. Since no heat is exchanged, any work done in an adiabatic process directly changes the internal energy and therefore the temperature of the system.
The isobaric process is characterized by maintaining a constant pressure (\(P\)) throughout the change. During an isobaric process, all three other variables—volume, temperature, and internal energy—are free to change as the system does work or exchanges heat.
Finally, the isochoric process is one where the volume (\(V\)) remains constant. Because volume is fixed, the system can do no work, meaning that any heat added or removed goes entirely into changing the system’s internal energy and, consequently, its temperature.