# What is an isothermal process with an example?

Jul 31, 2016

An isothermal process is one for which $\Delta \text{T} = 0$, where $\Delta \text{T}$ is the temperature change of the system.
Consider a phase change under constant temperature, as induced by a pressure change. Consulting any phase diagram will show you that multiple phases, or even allotropes, of a species may exist at a given temperature $\text{T}$. Let's take the phase diagram of carbon, with main allotropes of graphite and diamond, as an example.
This phase diagram demonstrates a triple point - conditions that cause a sample to exhibit three of its states of matter - at a pressure of 10.8 ± 0.2 "MPa" and a temperature of 4,600 ± 300 "K". Theoretically, if the temperature is controlled and pressure is varied either side of this point, one may freeze or evaporate the sample at will without temperature acting as a variable factor.
As a contrasting side note, a distinction can be made between an isothermal process and an adiabatic one. In the case of the latter heat cannot be transferred to or from the surroundings, although $\Delta \text{T}$ for the system may be a non-zero value as a result of work being done. On the other hand, the former specifies that $\Delta \text{T} = 0$ within the system at all times, but this term also refers to setups in which there is a heat transfer that inhibits a net temperature change.