# Thermodynamics - Stirling Engine

• Feodalherren
In summary, Stirling engines have been around since 1816 when Robert Stirling, a Scottish clergyman, patented the design. It uses external combustion to heat one of two cylinders, with a fixed amount of inert gas moving between them and expanding in the hot cylinder and contracting in the cold one. It can be used to efficiently convert various forms of energy, such as burning garbage and solar energy, into mechanical work. However, it is not commonly used as an engine for cars due to various factors such as its lower efficiency compared to internal combustion engines and turbines, and the complexity and cost of manufacturing.
Feodalherren

## 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 cylinders, expanding in the
hot one and contracting in the cold one. Consider
n mol of an ideal monatomic gas being taken once
through the cycle, consisting of two isothermal processes
at temperatures 3Ti and Ti and two constant-volume
processes. Determine in terms of n, R, and Ti (a) the net
energy transferred by heat to the gas and (b) the efficiency
of the engine. A Stirling engine is easier to manufacture
than an internal combustion engine or a turbine.
It can run on burning garbage. It can run on the energy
of sunlight and produce no material exhaust.

w=-∫PdV
e= w/Qh

## The Attempt at a Solution

So for part b I'm a little bit confused as to how to calculate work.

Since two of the processes are isovolumetric the work done by them = 0.
Now this is where I get confused. Doesn't the isothermal process that represents a decrease in the volume translate to work done ON the gas - therefore it should be positive. The solutions manual lists them both with the same sign. If I add my work together I do get the same result (-nRTi ln(4)). So my question I suppose is more conceptual.
How does a decrease in volume represent work done by the engine?

Doesn't the isothermal process that represents a decrease in the volume translate to work done ON the gas - therefore it should be positive.
http://en.wikipedia.org/wiki/Stirling_cycle
http://en.wikipedia.org/wiki/Thermodynamic_cycle
... that's how it would normally go.

The solutions manual lists them both with the same sign.
...
compare:
http://physics.stackexchange.com/questions/78915/efficiency-of-stirling-engine-and-carnots-theorem

The minus and plus signs are not things you plug in, they come out of the definition of mechanical work.

1 person
Ah that makes sense. Thank you again Simon!

No, I know the signs come from the definition but I was getting confused as to what was going on. Now that I've seen HOW a Stirling engine works it makes sense. I didn't really understand it in class when the professor was showing examples.

They are kinda fun to build too...
... anyway - well done :)

Yeah I really want to give it a shot. If I have time this summer I will attempt to build one that runs between the temperature difference of ice and a warm room :).

Gyes
can we use this engine for daily uses??

Depens on the uses.
There are commercial stirling engines for eg.

But ,can it be more efficient than commercial one?

Depends on the commercial one you want to compare it with.
There will almost certainly be commercial sterling engines that are more efficient than one you can build yourself - but I don't know you, it may be that you have access to a high tech engineering lab.

Last edited:
Thanks simon,

Actually i am working on stirling engine project in which at primary stage we are trying to know

"why stirling engine Is not first choice for car engines"

so ,
can u there to help me?

Stirling engines are not practical for car engines. Part of the project is, presumably for you to discover why.
To do that you need to figure out what the special advantages would be and then examine actual engines to compare.
An equally valid question which sheds light on your one is why the internal combustion engine is preferred for cars in the first place.

Quite a lot has been written on why Stirling engines are not in more widespread use and when you build one you'll probably discover several of the reasons for yourself. It took me less than a day of googling to answer your questions: our time here is better spent dealing with where you don't understand the existing writing than repeating it.

## 1. What is a Stirling engine?

A Stirling engine is a type of heat engine that converts thermal energy into mechanical work. It operates by cyclic compression and expansion of air or other gas at different temperatures, resulting in a net conversion of heat energy into mechanical energy.

## 2. How does a Stirling engine work?

A Stirling engine works by using a fixed amount of gas, typically air, that is sealed inside a closed container. The engine has two pistons, one hot and one cold, connected to a crankshaft. As the gas is heated by an external heat source, it expands and pushes the hot piston, which in turn moves the crankshaft. The gas is then cooled, causing it to contract and pull the cold piston back, completing the cycle.

## 3. What are the advantages of a Stirling engine?

Stirling engines have several advantages over traditional combustion engines, including greater efficiency, lower emissions, and the ability to use a variety of heat sources. They also have fewer moving parts, making them more reliable and easier to maintain.

## 4. What are the applications of Stirling engines?

Stirling engines have a wide range of applications, including power generation, heating and cooling systems, and even transportation. They are also used in renewable energy systems, such as solar power plants, where they can convert solar energy into electricity.

## 5. What are the limitations of Stirling engines?

One of the main limitations of Stirling engines is their low power-to-weight ratio, which makes them less suitable for applications that require high power output. They also have a slower startup time and require precise engineering and manufacturing, making them more expensive compared to other types of engines.

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