Stirling Definition and 80 Threads

Stirling (; Scots: Stirlin; Scottish Gaelic: Sruighlea [ˈs̪t̪ɾuʝlə]) is a city in central Scotland, 26 miles (42 km) north-east of Glasgow and 37 miles (60 km) north-west of the Scottish capital, Edinburgh. The market town, surrounded by rich farmland, grew up connecting the royal citadel, the medieval old town with its merchants and tradesmen, the Old Bridge and the port. Located on the River Forth, Stirling is the administrative centre for the Stirling council area, and is traditionally the county town of Stirlingshire. Proverbially it is the strategically important "Gateway to the Highlands".
It has been said that "Stirling, like a huge brooch clasps Highlands and Lowlands together". Similarly "he who holds Stirling, holds Scotland" is often quoted.
Stirling's key position as the lowest bridging point of the River Forth before it broadens towards the Firth of Forth made it a focal point for travel north or south.When Stirling was temporarily under Anglo-Saxon sway, according to a 9th-century legend, it was attacked by Danish invaders. The sound of a wolf roused a sentry, however, who alerted his garrison, which forced a Viking retreat. This led to the wolf being adopted as a symbol of the town as is shown on the 1511 Stirling Jug. The area is today known as Wolfcraig. Even today the wolf appears with a goshawk on the council's coat of arms along with the recently chosen motto: "Steadfast as the Rock".Once the capital of Scotland, Stirling is visually dominated by Stirling Castle. Stirling also has a medieval parish church, the Church of the Holy Rude, where, on 29 July 1567, the infant James VI was anointed King of Scots by Adam Bothwell, the Bishop of Orkney, with the service concluding after a sermon by John Knox. The poet King was educated by George Buchanan and grew up in Stirling. He was later also crowned King of England and Ireland on 25 July 1603, bringing closer the countries of the United Kingdom. Modern Stirling is a centre for local government, higher education, tourism, retail, and industry. The mid-2012 census estimate for the population of the city is 36,440; the wider Stirling council area has a population of about 93,750.One of the principal royal strongholds of the Kingdom of Scotland, Stirling was created a royal burgh by King David I in 1130. In 2002, as part of Queen Elizabeth's Golden Jubilee, Stirling was granted city status.

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  1. kenobiobiwan66

    Energy Production through Stirling Engine?

    A Beta-Type Regular Low Temperature Striling Engine being used to produce mechanical energy, where hot water at 350K is being used as fuel. What power should one expect theoretically?
  2. Pythagorean

    Stirling Engines for Home Power

    Would it be a feasible power source to have several Stirling Engines sticking through an outdoor wall near your fire place in a cold climate? Issues I can think of: Presumably it would be a heat sink and require you to consume more firewood. Engineering it to not have passive leaks might be...
  3. C

    I Ideal working gas for a Stirling engine

    I was reading around Stirling engines and there's something I am not sure about, can't see a logical explanation. So the ideal gases discussed are hydrogen and helium on account of their higher thermal conductivities. But I am unclear on what motivation there would be to use hydrogen which has...
  4. alwaystiredmechgrad

    I Defect concentration formula w/o Stirling approximation

    In many cases, the concentrations of defects or charges are quite big enough to use SA, due to a big number of Avogadro's number. The derivation for the well-known formula of a defect concentration is followed. If the n_v is expected to be lower than 1, then it would be impossible to use SA...
  5. D

    B Can a Heat Pump and Stirling Engine Create a Perpetual Energy Cycle?

    I was reading about heat pumps and it made me wonder… would the following process be physically possible…? I attach the hot side of the heat pump to the hot side of the stirling engine. 400% COP (coefficient of performance) means 1 kilowatt hour of electricity consumed by the heat pump delivers...
  6. L

    I Simplifying limit with Stirling approximation

    I'm trying to determine why $$ \lim_{N \rightarrow +\infty} ln( \frac {N!} {(N-n)! N^n}) = 0$$ N and n are both positive integers, and n is smaller than N. I want to use Stirling's, which becomes exact as N->inf: $$ ln(N!) \approx Nln(N)-N $$ And take it term by term: $$ \lim_{N...
  7. J

    Stirling engine LTD (Low Temperature Differential) plate size / energy

    i need a simple calculation of a stirling ltd surface area calculation per watt produced and would a very rough surface and very large surface area hinder heat flow if the distance to re generator is extreme /would folding the surface area of a flat plat ltr help increase the power of engine...
  8. Isolde Wilde

    How Does Heat Affect the Motion of a DIY Stirling Engine's Wheel?

    hello, I had made an DIY alpha type Stirling engine for my physics project and now I have to write an report about the relationship between the heat given to the engine and the motion of the wheel. I had searched a lot about Stirling engines and I learned about work, energy, efficiency...
  9. Mr Davis 97

    Computing S(n,3) Stirling number of 2nd kind

    Homework Statement Compute ##S(n,3)##. Homework EquationsThe Attempt at a Solution To compute this I used the fact that ##S(n,2) = 2^{n-1}-1## and used the recurrence relation ##S(n,k) = kS(n-1,k) + S(n-1,k-1)##, and used induction to get that ##S(n,3)=\frac{3^{n-1}+1}{2}-2^{n-1}##. But is...
  10. A

    MHB How to proof stirling approximation

    i want to know about stirling approximation. why lnx! = xlnx - x
  11. H

    I Is this a Stirling number of the second kind?

    I saw this paper that talks about phonon sidebands, multiphonon relaxation, and phonon-assisted energy transfer. I was skimming through each of the equations, but I have problem understanding the formulation of some of them, for example Equation (3.17): g_{\pm }(t) = \int d\omega...
  12. Waggles

    Renewable Energy Concept - Stirling Engine Composting

    So I've got this crazy idea. To put it simply, to use the heat from anaerobic composting to power hot-air engine, specifically a Stirling Engine. Based solely on my own reading, the center of a closed composting heap can reach anywhere from 120-160 degrees without killing the microorganisms...
  13. Jarro

    Stirling engine against solar panels

    Hello, Since childhood, I have been wondering why it is not possible to make miniature electric motors with pistons and gas container covered with a very dark (meaning high absorption coefficient over a wide spectral width) material that would translate the energy of sunlight directly into...
  14. G

    Error in this depiction of a Stirling engine?

    Hi. In my (German) physics lecture notes, I found this depiction of a Stirling engine: According to the text, it should be A: isothermal expansion B: isochoric cooling C: isothermal compression D: isochoric heating This seems correct for the PV diagram, but strange in the illustration on the...
  15. G

    Stirling cycle: Why neglect isochoric heat transfers?

    Hi. To prove that the Stirling cycle has Carnot efficiency, one needs to neglect the isochoric heat transfers. Sure they have the same absolute value (but different signs), but it's still heat energy lost to the cold reservoir during the isothermic compression.
  16. G

    I Gibbs paradox for a small numbers of particles

    Hi. Trying to solve the Gibbs paradox for two identical volumes of ideal gas with ##N## particles each, I found the mixing entropy to be $$\Delta S=2N \log(2)-\log((2N)!)+2\log(N!)\enspace .$$ The usual approach now uses Stirling's approximation to the order ##\log (n!)\approx n\log (n)-n##...
  17. TheBigDig

    Finding the work done by a Stirling Cycle

    1. Given the following p-V diagram of an ideal Stirling Cycle, determine the theoretical values of W12, Q12, W34 and Q34 in terms of T1, T2, V1, V2, n (the number of moles) and R (the universal gas constant). Determine the total theoretical p-V work W12341 for the full cycle.2. dU = dQ-Pdv3...
  18. TheBigDig

    Finding the energy dissipated per cycle in a Stirling Engine

    1.Recently, we performed an experiment to measure the efficiency of the Stirling Engine. The experimental method can be seen in the image provided. We have been asked to calculate the power dissipation PR and the energy dissipation per cycle WR as part of our lab report. The other variables...
  19. Hercuflea

    Why do Stirling engines have low power/weight?

    I have heard that Stirling engines are not in wide use because they have a low power-weight ratio. Why is this? It would seem to me that the Beta type stirling engine (with 1 cylinder) would be very efficient because it only has like 3 major moving parts...flywheel crankshaft and piston and...
  20. W

    Cryocooler Stirling 1-stage build, some questions

    Hello everyone! Just the forum I was hoping to find! There are really not many ppl to ask about this subject.Had nothing to do about a month ago so I thought that it would be quite fun and interesting to build a cryocooler, it will be a long time project though since I lack many things right...
  21. M

    How to Calculate Energy and Work in a Stirling Cycle?

    Homework Statement Suppose that 282 moles of a monatomic ideal gas is initially contained in a piston with a volume of 0.81 m^3 at a temperature of 574 K. The piston is connected to a hot reservoir with a temperature of 1365 K and a cold reservoir with a temperature of 574 K. The gas undergoes...
  22. sophiecentaur

    Which is the best fan for my wood burning stove: Peltier or Stirling?

    I am having a wood burning stove installed soon. I am wondering which would be better, to put on the top and aid room circulation, an electric fan, powered from a Peltier junction or one using a Stirling Engine. Does anyone have any ideas or experience about this? I wouldn't expect 'efficiency'...
  23. C

    What is the Stirling transform of (k-1)?

    While reading about combinatorial mathematics, I came across the Stirling transform. https://en.wikipedia.org/wiki/Stirling_transform So then, if I want to find the Stirling transform of, for instance, ##(k-1)!##, I have to compute this (using the explicit formula of the Stirling number of the...
  24. E

    How to simplify using stirling approximation?

    Hey! So we're deriving something in Daniel Schroeder's Introduction to Thermal Physics and it starts with this: \Omega \left( N,q\right) =\dfrac {\left( N-1+q\right) !} {q!\left( N-1\right) !} Both N and q are large numbers and q >> N. The derivation is in the book, but I am always...
  25. CivilSigma

    Efficiency Calculation for a Stirling Engine Cycle

    Homework Statement Figure 2 represents a model for the thermodynamic cycle of the Stirling engine, patented by Scottish clergyman Robert Stirling in 1816. The engine operates by burning fuel externally to warm one of its two cylinders. A xed quantity of inert gas moves cyclically between the...
  26. D

    Stirling Approximation for a thermodynamic system

    Homework Statement The stirling approximation, J! = √JJ+1/2e-J, is very handy when dealing with numbers larger than about 100. consider the following ratio: the number of ways N particles can be evenly divided between two halves of a room to the number of ways they can be divided with 60% on...
  27. D

    Efficiency, Stirling heat engine

    Homework Statement We have a Stirling heat engine. I'm calculating the efficiency \eta. Homework Equations Q_{12} = \frac{m R T_2}{M} \ln(\frac{V_2}{V_1}) > 0 Q_{23} = m c_v (T_1 - T_2) < 0 Q_{34} = \frac{m R T_1}{M} \ln(\frac{V_1}{V_2}) < 0 Q_{41} = m c_v (T_2 - T_1) > 0 \kappa =...
  28. U

    Can Polystyrene Withstand the Heat in a Stirling Engine Displacer?

    Hey Guys, I'm working on a Stirling engine to show my nephew. I have made one before that runs off off coffee water but now I'm planning on making a system which will use a heat source around 90-125°C and I do not know if polystyrene will melt or not. So if you guys have any suggestions for a...
  29. M

    Efficiency of Stirling heat engines

    Not sure if this should be posted in the general physics forums or in the hw/coursework section. I'm in my second semester of general physics and have to do a class project. For my project I built an alpha type Stirling engine. In the paper I need to write I need to explain how it works using...
  30. Feodalherren

    Thermodynamics - Stirling Engine

    Homework Statement In 1816, Robert Stirling, a Scottish clergyman, patented the Stirling engine, which has found a wide variety of applications ever since. Fuel is burned externally to warm one of the engine’s two cylinders. A fixed quantity of inert gas moves cyclically between the...
  31. A

    How do you measure the force of a Stirling engine?

    I was wondering how the force of a Stirling engine was measured? I mean, for every degree Celsius that the temperatures differ. how much more force (or horse power) is the engine generating? Are there any other variables to this? What I'm getting is can Stirling engines power cars if enough heat...
  32. C

    Stirling Engine School Project Help

    I need to generate electricity from this, how would I do so? I was thinking about placing magnets on the flywheel and using silver wiring as a conductor. This needs to power an RC cars electric motor so I can drive the thing and I have little to no experience with anything electrical. Any...
  33. alyafey22

    MHB How to Prove Stirling Numbers of the First Kind for s(n,3)?

    HI folks , working on Stirling nums , how to prove ? s(n,3)=\frac{1}{2}(-1)^{n-1}(n-1)!\left(H_{n-1}^2-H_{n-1}^{(2)}\right) where we define H_k^{(n)}= \sum_{m=1}^k \frac{1}{m^n} I don't how to start (Bandit)
  34. H

    What is the purpose of using two cylinders in a Moriya Stirling engine fan?

    Hi all:I am currently considering building a moriya stirling engine fan turbine. I would like to know if anyone here has built one. If so, is it possible for you to explain why they use 2 cylinders (power and displacer)? what is the principles of using two cylinders over this type ...
  35. Hercuflea

    Where can I find resources for building stirling engines?

    Anyone have any good resources/how-tos on building miniature (or not so mini) stirling engines? They seem pretty simple to make, and the coke can ones are pretty cool.
  36. W

    Comparing Carnot efficiency to Stirling efficiency

    Homework Statement In the problem, we were to derive work and heat for each leg of the cycle. Then we are asked: In the definition of the efficiency of this cycle, η =W Qpos , where Qpos is the total positive heat flow to the engine, what is the efficiency of the cycle when Th = 700K and Tc =...
  37. W

    Calculating Work and State Variables for an ideal Stirling Engine

    Homework Statement Consider the ideal Stirling cycle working between a maximum temperature Th and min temp Tc, and a minimum volume V1 and a maximum volume V2. Suppose that the working gas of the cycle is 0.1 mol of an ideal gas with cv = 5R/2. A) what are the heat flows to the cycle during...
  38. tsuwal

    Horrible limit with factorials. Need to use Stirling formula?

    Homework Statement Homework Equations The Attempt at a Solution Do I need to used the boring Stirling formula?
  39. tsuwal

    Thermodynamics: Is Stirling engine reversible or irreversible?

    Stirling engine: the cycle is composed by two isothermals and 2 isometrica and there are just two heat reservoirs. By the isometrics I would say that that it is irreversible since you exchanging heat with a reservoir at a different temperature than your gas. However my notes say the...
  40. F

    Will curved heat pipes improve Stirling engine efficiency?

    Stirling engines use regenerators(heat pumps) to recover heat and increase their efficiency.The basic problem here is "The regenerator constitutes a (dead) volume which thwarts the benefit of its presence.There is never absolute truth" I believe I have a working concept of the heat pipe.My idea...
  41. D

    Readily-available radioisotope heat source for a Stirling engine?

    Hi folks...I'm new here, please go easy on me, it's been quite a long time since college physics! :-) I need a feasible and readily available heat source for a Stirling cycle engine. (It's a type of engine that runs off of hot air...google it and you'll see plenty of examples.) Is there a...
  42. A

    Design a Stirling Engine: Gamma vs. Beta

    I am thinking of building a Stirling engine and am debating between a gamma type and beta type. Any advice on which type I should go for, and what the advantages/disadvantages to each is? Thanks
  43. M

    The workings of a Stirling engine

    Hi As a school project, I want to construct a Stirling engine (particularly this kind : http://monsterguide.net/how-to-build-a-stirling-engine ). The execution is quite simple, but I do not fully understand the theoretical background. Can someone give me an explanation?
  44. B

    MHB Orthogonality of stirling numbers

    Dear MHB members, denote by $s_{n,k}$ and $S_{n,k}$ Stirling numbers of the first-kind and of the second-kind, respectively. I need to see the proof of the identity $\sum_{j=k}^{n}S(n,j)s(j,k)=\sum_{j=k}^{n}s(n,j)S(j,k)=\delta _{{n,k}}$. Please let me know if you know a reference in this...
  45. T

    Stirling Engine Help for High School Engineering Project

    I'm designing a stirling engine for a high school engineering project. I need to know more information about them though before I start machining out the parts. I looked at Wikipedia and a few other sites, but I need something a little more in depth. I'm looking for a good stirling engine book...
  46. T

    Stirling engine survey for high school engineering class

    I am making a CNC machined stirling engine for high school my engineering class. Before I can get started I need people to fill out this survey to help me decide which design to go with. Thanks! Stirling Info http://en.wikipedia.org/wiki/Stirling_engine...
  47. A

    Thermodynamics: Efficiency for Stirling engine

    Homework Statement I'm trying to find an expression for the efficiency of a stirling engine operating with an ideal diatomic gas, and cycling through a volume V and a multiple of its compression ratio, r, Vr. Homework Equations processes: 1-2 isothermal expansion 2-3 isochoric...
  48. M

    Why do you need to start this Stirling engine by hand?

    Homework Statement Why do you need to start this Stirling engine by hand? Homework Equations N/A The Attempt at a Solution there is not sufficient power at first to overcome the inertia, so external work in the form of pushing it by hand is needed. however once started the momentum of the...
  49. A

    Thoughts on Stirling engines as source of electrical power in space

    Curious your thoughts about the use of a Stirling engine to power a space station, auxiliary power for space ships inside the inner solar system, and power for space colonies in the inner solar system. I think a Stirling engine would be great to generate an electrical field, and thus provide...
  50. K

    Stirling Engine Theory - Mechanically Driven

    Hi, I have had an idea floating around regarding stirling engines, and was hoping that somone may be able to provide some information. Supposing a stirling engine is run mechanically, one side heats up, the other cools down. what would happen if the cool side was heated externally...
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