Stirling Definition and 80 Threads

I have problem with prooving those two identities. Any help would be much appriciated! Show that: a) \begin{Bmatrix} m+n+1\\ m \end{Bmatrix} = \sum_{k=0}^{m} k \begin{Bmatrix} n+k\\k \end{Bmatrix} b) \sum_{k=0}^{n} \begin{pmatrix} n\\k \end{pmatrix}...

CONJECTURE: Subtract the Absolute Values of the Stirling Triangle (of the first kind) from those of the Eulerian Triangle. When row number is equal to one less than a prime number, then all entries in that row are divisible by that prime number. Take for instance, row 6 (see below). The...

OK very crude first sketch let me try to explain and you tell me if it sounds remotely workeable. Likemany other eco nuts after the holy grail of energy, I'm trying to brainstorm a low cost solar CHP system. I'm of the opinion that passive solar is always going to win on a BTU/$ collected and...

Does anyone know what stirling engine could be used to power a generator which in turn powers an electric motor? I am thinking of using this concept in a vehicle. A diagram is here: It shows a metal sphere in vacuum sealed container. It would be connected to by a retractable contact...

There is a temperature difference and we know the transition of the working fluid (from the hot chamber to the cold one) is isometric. So either there must be a pressure difference, or the number of molecules must be smaller; however, this can't be the case since eventually all the gas must move...

Where should I post questions about how to make a DIY Stirling Engine work?

Hello all. I've been wanting to build a Stirling engine at home out of parts that i could easily afford/scrounge up. Not one of those small ones that you hold in your hand, but one that could generate some real work. Enough to run a small generator maybe. The problem is that i have absolutely no...

Hi Guys I m trying to make a Stirling engine power by solar heat. Somewhere I found out that the solar flux available on Earth is abt 1350watts/m2 Is this heat energy only or "heat & light " combined?? I m trying to find out if my soar engine will be better than traditional solar...

It does not sound bad, does not It??. Using the residual heat it would be possible to power a Stirling engine, producing energy to be stored in the battery. Getting less power from the gas engine, (less time alternator running), less gas used, higher efficiency. How does it sound??

Homework Statement I need some help with this problem: A model Stirling engine uses n = 7.44 × 10–3 mol of gas (assumed to be ideal) as a working substance. It operates between a high temperature reservoir at TH= 95.0°C and a low temperature reservoir at Tc = 24.0°C. The volume of its...

I am doing some experimental work with stirling enging design, in order to add supliment the power I use at my house, and want to get some facts straight, and throw out some ideas for discussion (or destruction, as the case may be) Basic assumptions:(so far) The more heat differential would...

not sure if anyone has seem this, but I think its a great way to add energy efficiency. http://www.msi.com/index.php?func=newsdesc&news_no=591 (and no i don't work for them) dr

I have been doing a bit of research on building a low temperature Stirling engine, and I came across this website, http://heetgasmodelbouw.ridders.nu/Webpaginas/pagina_koffiekop_jan/koffiejan_frameset.htm The design on this website looks nice, and I would like to give it a go (after I build a...

Hey, I'm an electrical engineering student and I'm trying to design a solar dish which converts the heat from sunlight into electricity. I managed to make a small stirling engine with the results i got from google (The stirling engines made from coke cans). I was wondering how costly...

Homework Statement Derive an expression for the effiency of the cycle (of a Stirling Engine) working between two heat baths at temperatures T1 and T2 with volumes in the ratio V2/V1. Assume the working substance is a monatomic ideal gas. Homework Equations Work done=heat absorbed from...

I have a pretty broad question. I, with several others, am working on some stirling engines for a science fair of sorts. I have done enough research to understand the concept of how they work. I also understand that there are several different types; single cylinder, double cylinder etc. What I...

How to prove that this formula is correct: \lim_{x\to\infty} \frac{\Gamma(x+1)}{\sqrt{2\pi x}\big(\frac{x}{e}\big)^x} = 1 I have seen a proof for this: \lim_{n\to\infty} \frac{n!}{\sqrt{2\pi n}\big(\frac{n}{e}\big)^n} = 1 but it cannot be generalized easily for gamma function. The proof...

Need clarification of some thermodynamic concepts dealing with a Stirling engine. I've read descriptions that talk about the temperature of the heat source. Is this temperature referring to the surface temperature of the metal that contains the gas? Or is it referring to the temperature of...

Homework Statement Show that the integrand of \Gamma(s+1)=\int_{0}^{\infty} t^se^{-t}dt may be written as e^{f(t)} where f(t)=s\ln{t}-t. Show that f(t) is maximum at t=t_0 and find t_0. If the integrand is sharply peaked, expand the integrand about this point (ie Taylor expansion) and...

While toying with the factorial function, I stumbled with the following definition: Let P_k^{\,n} be the sum of all possible products of k different factors, taken from {1,2,3,...n}. For example, P_3^{\,4} = 1.2.3 + 1.2.4 + 1.3.4 + 2.3.4 = 50 Now, according to the Sloane site, this guys turn...

I've heard that solar water heating is very efficient, almost all the radiation of the sun on the panel is turned into heat. Also heard Stirling cycle generators (where heat flow from hot to cold is turned into mechanical motion and hence into electricity) are also quite efficient. Though by...

Hello, I am working toward my new Stirling engine prototype for a particular application. Let me start with a small description of what I am going to try anyways: I will experiment this with a small electrical heater: - heat input: 50-100 W (heater thermall insulated on all sides but the...

Homework Statement f(1)+f(2)...+f(n-1) =< \int_{0}^{n} f(x) dx =< f(2) +f(3)+...+f(n) is increasing and continuous on [1, inf) I'm meat to prove the above, the idea I had was to use the trapezium rule to get an approximation of the integral, but since f''(x) can be either negative or positive...

Halliday says that the efficiency of an ideal Stirling engine is lower than that of a ideal Carnot engine?? But why?? It seems to me that there efficiency are both \epsilon =1-\frac{T_L}{T_H} Though Halldiay also say that this equation do not apply to Stirning engine but only to Carnot...

Hello everyone i was wondering if someone could check to see if this looks correct or not. The question is: If X is a set with n elements and Y is a set with m elements, express the number of onto functions from X and Y using Stirling numbers of the second kind. Justify your answer. note: the...

Hi, *** for the ones that don't like to read much (:smile:): the basic point is that I need a gas that gives as much pressure as possible with a temperature increase and a constant volume and that is easy to get my hands on; and a liquid with a high density (like mercury or something) that...

Hi. I know of the commercially available "battery-less" flashlights that use either squeezing or shaking mechanisms to generate electricity. I was wondering, however, whether I can create one that uses the difference of temperature between the hand and the room temperature. I propose to use a...

I've calculated the efficiency of the Stirling cycle like \eta=\frac{R(T_H-T_L)\ln\left(V_2/V_1\right)}{RT_H\ln\left(V_2/V_1\right)+C_{mV}(T_H-T_L)} Where V_2>1. It's also derived http://www.pha.jhu.edu/~broholm/l39/node5.html" . But my ("Highschool", or secondary school) teacher says...

Hello again, I need to prove the following identity for Stirling numbers of the first kind: s_{n,2} = (n-1)!\Big(1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n-1}\Big) For the uninitiated, s_{n,k} is a Stirling number of the first kind and represents (as I was explained) the number of...

[SOLVED] Stirling Engine Information Just want to make sure everyone is aware that the Stirling engine is advancing and has many great applications in power/energy generation, cooling, and water purification. http://www.StirlingInfo.com has current news, and an organized directory.