## Sections on the page :Abstract ## AbstractThis page contains a short rehash of the Stirling cycle for heat engines. Some math and knowledge of thermodynamics ( conservation of energy , internal energy , specific heat capacities at constant pressure and constant volume ) is required for understanding. Major finding, beyond what can practically be found in any text book, is that the heat transfer load on the regenerator is influenced by the gas being used through the value of the gas' ratio of specific heats. The heat load on the regenerator increases as we go from monatomic to diatomic gases by a factor of 1.67 and by a factor of more than 2 as the gas molecules contain 3 or more atoms.Back to top ## IntroductionThe ideal Stirling Cycle consists of 4 individual processes with end points as marked in the p-V diagram ( p=pressure, V=volume). Its analysis is a standard item in all text books of engineering thermodynamics dealing with gas powered heat engines. So why revisited ? Apart from summarizing the underlying thermodynamic laws and the resulting equations we look at the heat transfer needed for the two isochoric processes of the cycle and the amount of heat needed to facilitate them. Surprisingly, the amount of heat needed for these processes depends strongly on the ratio of the specific heats of the working fluid favoring monatomic ideal gases to be used as working fluid. The term "fluid" is used here in the same way physicists use it : it can mean either a gas or a liquid.Back to top ## Description of Cycle
_{12}, from the working fluid in order to keep
the temperature at a constant low value, T_{C}.
This is followed by an isochoric compression (process 2→3). The latter
takes place because heat of the amount Q_{23} is added to the working
fluid. Expansion (process 3→4) takes place at constant temperature, T_{H}.
In order to keep the temperature constant, heat, Q_{34}, has to be
added to the working fluid. Finally, the pressure is lowered at constant
volume by removing heat, Q_{41}, from the working fluid to close
the cycle.
## The Regenerator and Efficency of Stirling CycleBasis of the analysis of a cycle is the 1. law of thermodynamics of all its sub processes. In this case we have a working fluid of constant mass which for a process with starting point i and end point j is :
Q with :
Q
W U In particular, for the process 2→3 the volume does not change and
therefore W Q and similarily for the process 4→1 : Q If we choose a working fluid for which the internal energy depends
only on temperature ( liquids and ideal gases for example ) the
internal energies U Q Or in other words, the heat we have to remove from the gas during the
process 4→1 can be used to heat the gas during the process 2→3,
which is exactly the function of the Once a regenerator is employed, the interaction of a Stirling engine with its
surrounding is restricted to receiving heat at temperature T η = 1 - T Back to top ## Influence of working fluid on work and heat transfer ratesWe assume that our working fluid is an ideal gas with constant specific heat capacities. Hence for the process 3→4 the internal energy of the gas remains constant and :
Q In the same fashion for the process 1→2 :
Q And the network per cycle :
W The heat supplied at temperature T η = 1 - T This is standard thermodynamic stuff and nothing new. We wish to take a look
though at the influence of changing the working fluid, for example He vs.
H n = (p With that, the numerical values for the above works, heats, and the efficiency are not affected by a change of gas. The story is different though for the regenerator. The heat transferred from the regenerator material into the gas during the process 2→3 and removal from the gas during 4→1 is equal to the change in internal energy of the gas which for constant specific heat capacities is : Q Q
^{*} Factor = factor by which the heat load on the regenerator
increases
in comparison to the case of having a monatomic gas.
Back to top |

Last revised: 12/05/14