Steam Engine work application problem

In summary, the conversation discusses how to find the work done by a steam engine during a cycle using the equation PV^1.4=k. The participants start by trying to find the constant k and then discuss the use of different formulas and variables. They also mention an article that explains how to integrate the equation and calculate work based on initial pressure and volumes.
  • #1
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Homework Statement


In a steam engine the pressure and volume of steam satisfy the equation PV1.4=k, where k is a constant. Calculate the work done by the engine (in ft/lbs) during a cycle when the steam starts at a pressure of 100 lb/in2 and a volume of 400in3 and expands to a volume of 1100in3.

Homework Equations


Use the fact that the work done by the gas when the volume expands from volume v1 to volume v2 is:

W=∫V2v1 P dV



The Attempt at a Solution



As usual, getting hung up on where to start. So I tried to find k. Solving for k at the starting pressure of 100lb/in2 and volume of 400in3 I get a k=439,424.2

That # seems way high. Is the problem assuming the pressure is starting at these values (100lb/in2 and 400in3)??

Thanks
 
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  • #3
interesting... now I'm even more confused!
 
  • #4
Our professor didn't say we needed any special formulas or anything - that we should know how to do this from our previous section's lessons. Where do I start? That link shows more variables than I have (I think) like lambda values, etc.
 
  • #5
Please, any help would be appreciated. I'm not looking for an answer, just a push in the right direction. Here's what I've tried to do to start out:

-put integral in terms of V
-break down Volume values and try to solve for r and h
-ratio between starting values: 100lb/in^2 and 400in^3

?
 
  • #6
The attached article shows how to integrate P dV when PV^gamma = k (Note: there are no lambdas present.) Work is explicitly given in terms of initial pressure and initial and final volumes. (See section "Derivation of discrete formula")
 

1. How does a steam engine work?

A steam engine works by using coal or other fuel to heat water in a boiler, creating steam. The steam then moves through pipes and into a cylinder, pushing a piston back and forth. This motion is converted into rotary motion by a crankshaft, which can power machinery or turn wheels.

2. What is the purpose of a steam engine?

The main purpose of a steam engine is to convert the energy from the steam into mechanical work, such as powering machinery or transportation. It played a crucial role in the Industrial Revolution and was one of the first sources of power for factories and trains.

3. What are the advantages of using a steam engine?

Some advantages of using a steam engine include its ability to produce a constant and reliable source of power, its efficiency in converting heat energy into mechanical work, and its flexibility in being able to power various types of machinery.

4. What are some common problems with steam engine applications?

Some common problems with steam engine applications include boiler explosions, boiler corrosion, and issues with the seals and valves. These problems can be caused by improper maintenance, overworking the engine, or using low-quality materials.

5. How has the steam engine evolved over time?

The steam engine has evolved significantly since its invention in the 18th century. It has become more efficient, safer, and more versatile. The development of the steam turbine and the use of steam in electricity generation have also greatly impacted its evolution.

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