18 Due 12/2

Open-ended design question:

How could you, based on your knowledge of efficiencies and thermo, improve the performance of the lab Stirling engine with primarily thermodynamic (as opposed to mechanical) improvements? Discuss in detail. Explain the thermodynamics background behind your proposals clearly.

While your proposed improvement(s) must be thermodynamic in nature to qualify for credit in a thermo class, you must also discuss how to actually make the improvement in the lab engine. Include a design drawing.

Note that normally performance should be taken to be efficiency. If you take performance to be produced power, the obvious (and correct) answer is: make the engine bigger or build two of them. That trivial answer gets no credit. What we really want to see is nontrivial, creative (if at all possible), effective, fully explained and researched, improvements. There is some flexibility in what you define as efficiency, but you better argue your case solidly!

Come to think of it, it is your responsibility to convincingly argue, to any reasonably fair grader, that your modifications will work, to a nontrivial extent. It is not up to the grader to prove your idea(s) wrong. It is up to you to prove it/them right. Your evidence should be able to convince even the most sceptical, but scientifically fair, judge.

To do so, please remember two key facts from physics and one from this class:

• Under the same $P$, $V$, and $T$, different gasses have the same number of molecules (as in $PV=n\bar{R}_uT$). The mass of the gases will be different depending on what the molecular mass is. But who cares what the mass is; the mass of the gas is negligible compared to the mass of the engine anyway. So you must compare gas properties on a molar (number of molecules), not mass basis. The numbers in table A.5 are on a mass basis (note the kg in the bottom) and are not suitable for comparisons of working gases in engines.
• All ideal gases have the same translational kinetic internal energy $\frac{3}{2}k_{\rm {B}}T$ per molecule, (not per unit mass). And it is this translational kinetic energy that produces the pressure. For noble gases, the translational kinetic energy is all there is. However, diatomic gasses like air, hydrogen, nitrogen, and oxygen have at normal temperatures another $k_{\rm {B}}T$ of rotational kinetic energy per molecule. A more complex molecule like water has another $\frac{1}{2}k_{\rm {B}}T$. A flappy (i.e big and flexible) molecule may have much more internal kinetic and potential energy still. It does not help creating pressure.
• The efficiency of an ideal Stirling cycle with complete regeneration is
  
  $$\eta_{\rm th} = 1 - \frac{T_{\rm L}}{T_{\rm H}}$$
  
  
  See any pressures in there? Heat conduction amounts? Gas or other substance properties? If not, modifying these quantities can do nothing for the efficiency of the ideal engine. So if your proposal includes modifying any of these quantities, you must make clear what non-ideal effect will be improved by your modification.

Your proposal should be neat, easy to read, and formulated in a logical order: abstract, background, theoretical justification of the proposal, proposed implementation method with design drawing, and references.

An abstract is not an introduction. It must summarize what your final proposal is, and how it is to be implemented.

All sources used in your project must be referenced and fairly credited for their contributions. Violations of this rule are unethical. You are still responsible for understanding and verifying the claims you find in literature and on the web.

Any nontrivial claim made in your text must either give a freely available reference that verifies the claim, or you must prove the claim yourself. Not doing so will lead to major grade reduction.

All references cited in the text must be listed in alphabetical order in a references section at the end of the document (with author names, title, link, if any). This may also include other references you looked at and found helpful.

A couple of typed single-spaced pages plus a design drawing and a list of references is typical. And about the most Dr. Van Dommelen will look at.