Help with Calculating Work Done by a Model Stirling Engine

In summary, the problem involves a model Stirling engine operating between a high temperature reservoir at 95.0°C and a low temperature reservoir at 24.0°C. The engine uses 7.44 × 10–3 mol of gas and the volume of its working substance doubles during each expansion stroke. The engine runs at a rate of 0.6 cycles per second and the question asks for the work done per cycle. Using the formula W=nRT ln (Vi/Vf), it is determined that the work done for each leg of the cycle must be calculated and then added together to find the total work. Additionally, if asked for the power of the engine, the total work calculated should be multiplied by the number of cycles
  • #1
roam
1,271
12

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 working substance doubles during each expansion stroke. It runs at a rate of 0.6 cycles per second. Assume the engine is ideal.

How much Work does the engine do per cycle (include the sign)?

Homework Equations



[tex]W=nRT ln \frac{V_i}{V_f}[/tex]

The Attempt at a Solution



Using the formula above I get

(7.44 × 10-3)(8.314) T ln (vi/2vi)

But I don't know how to continue since I don't know the value for the initial volume or temprature and I don't know how to find them... I mean for the temprature at least, I'm given two different tempratures TH and Tc and I don't see which one to use!
 
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  • #2
The volume doubles, so Vi/Vf = 1/2 for the expansion processes and Vi/Vf=2 for the compression process.

Take a look at this graph: http://upload.wikimedia.org/wikipedia/commons/2/25/Stirling_Cycle.svg

You have to calculate the work done for each leg and add them together to calculate total work. The expansion/compression legs are isothermal, so there's only one T.
 
  • #3
ideasrule said:
The volume doubles, so Vi/Vf = 1/2 for the expansion processes and Vi/Vf=2 for the compression process.

Take a look at this graph: http://upload.wikimedia.org/wikipedia/commons/2/25/Stirling_Cycle.svg

You have to calculate the work done for each leg and add them together to calculate total work. The expansion/compression legs are isothermal, so there's only one T.

THANK YOU! It makes perfect sense now. :smile: But I have another question; what if they ask 'what is the Power of the engine?'

Should we just divide the total work done (that we just calculated) by the number of cycles per second? I tried that but it didn't give me the correct answer...
 
  • #4
You should multiply the work with the number of cycles per second, cause P = Q/t and Q = W(one cycle) * (cycles in a second) if t = 1 sec.
 

1. What is work done by a Stirling engine?

The work done by a Stirling engine is the amount of energy that is converted into mechanical work. This can be calculated by multiplying the force applied by the distance the force is applied over, also known as the work-energy principle.

2. How is work done by a Stirling engine calculated?

To calculate the work done by a Stirling engine, you need to know the force applied to the piston and the distance the piston travels. The formula for work is W = F * d, where W is the work done, F is the force applied, and d is the distance traveled.

3. Can the work done by a Stirling engine be negative?

Yes, the work done by a Stirling engine can be negative if the force applied is in the opposite direction of the piston's movement. This means that the engine is actually doing work on its surroundings, rather than work being done by the engine.

4. What factors affect the work done by a Stirling engine?

The amount of work done by a Stirling engine is affected by several factors, including the temperature difference between the hot and cold reservoirs, the type of gas used, the size and design of the engine, and any friction or losses in the system.

5. How can the work done by a Stirling engine be increased?

The work done by a Stirling engine can be increased by increasing the temperature difference between the hot and cold reservoirs, using a more efficient gas, and reducing friction and losses in the system. This can be achieved through design improvements and using high-quality materials.

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