When is gas compression isentropic

The ideal Brayton cycle consists of four thermodynamic processes. Two isentropic processes and two isobaric processes. As can be seen, we can describe and calculate e.

See also: Thermal Efficiency of Brayton Cycle. Isentropic Process. Search Search. Nuclear and Reactor Physics: J. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed.

Lamarsh, A. Baratta, Introduction to Nuclear Engineering, 3d ed. Glasstone, Sesonske. Nuclear and Particle Physics. Since there is no heat transferred into the cylinder and no other losses, the change in entropy is zero. Then the equation becomes:. We divide both sides by "cp" and take the exponential function of both sides this "un-does" the logarithms.

During the compression process, as the pressure is increased from p1 to p2, the temperature increases from T1 to T2 according to this exponential equation. For air, at standard conditions, it is 1. So if the pressure doubled, the temperature ratio is 1. The key point here is that we have a function that relates the temperature change to the pressure change during a compression process. We can use the equation of state to derive the relation between the volume change and the pressure change.

The equation of state is:. If we substitute this expression for T into the temperature equation, we obtain:. If compression or expansion of gas takes place under constant temperature conditions - the process is said to be isothermal.

The isothermal process can be expressed with the Ideal Gas Law as. If compression or expansion of gas takes place with no flow of heat energy either into or out of the gas - the process is said to be isentropic or adiabatic. The isentropic adiabatic process can be expressed with the Ideal Gas Law as. An ideal isothermal process must occur very slowly to keep the gas temperature constant. An ideal adiabatic process must occur very rapidly without any flow of energy in or out of the system.

In practice most expansion and compression processes are somewhere in between, or said to be polytropic. Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro.

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