Thermodynamics - Stirling Engine

[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.

Homework Equations

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?

 

[Simon Bridge]

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.

 

[Feodalherren]

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.

 

[Simon Bridge]

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

 

[Feodalherren]

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 :).

 

[Sanky123]

Gyes
can we use this engine for daily uses??

 

[Simon Bridge]

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

 

[Sanky123]

But ,can it be more efficient than commercial one?

 

[Simon Bridge]

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.

 

[Sanky123]

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?

 

[Simon Bridge]

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.