Isochore (volume)

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Figure 1. The PV diagram of an isochoric process

An isochore in the context of thermodynamics refers to any process in which the system remains at a constant (unchanging) volume. An isochoric process is modeled on a pressure volume diagram (PV diagram) as seen in Figure 1. For this process to be possible, the ideal gas must be in a rigid container that doesn't change in volume or let any molecules escape.


During an isochoric process, if heat is added to the system it will be absorbed as internal energy. The ideal gas law [math]pV=nRT[/math] states that increasing the internal energy (also known as temperature) will increase the pressure. If heat is removed from the system, the internal energy will decrease, and thus the pressure will decrease.


Since the volume of the system is not changing, no pressure-volume work is done by or on the system.[1] This can be seen visually on the pressure-volume diagram (figure 1), as there is no area under the curve (since work is found by calculating the area under the curve).


[math]W = 0[/math] when the volume of the system is constant.


One mechanism that uses the isochoric process is in heat engines that use diesel and gasoline. The waste heat is expelled right after the vehicle or machine receives power from combustion, but since the piston is not moving, the volume of the chamber is unchanging and the pressure drops. The process a gasoline engine undergoes is modeled by the Otto cycle (Figure 2) and diesel engines are modeled by the Diesel cycle (figure 3).

An isochoric process is seen in steps 2 to 3 and steps 4 to 1 in a Otto cycle, and in steps 4 to 1 in the Diesel cycle.


For Further Reading

References

  1. R. Knight, Physics for scientists and engineers. Boston, Mass.: Addison-Wesley, 2012, p. 474
  2. Wikimedia Commons [Online], Available: https://en.wikipedia.org/wiki/Otto_cycle#/media/File:P-V_Otto_cycle.svg
  3. "File:Grafico p-v.JPG - Wikimedia Commons", Commons.wikimedia.org, 2018. [Online]. Available: https://commons.wikimedia.org/wiki/File:Grafico_p-v.JPG. [Accessed: 10- Jul- 2018].