Calculating Work Done by a Steam Engine Using Integral Calculus

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SUMMARY

The discussion focuses on calculating the work done by a steam engine using integral calculus, specifically through the equation PV1.4 = k, where k is a constant. The work done is expressed as W = ∫V1V2 PdV, with given values P1 = 160 lbs/in2, V1 = 100 in3, and V2 = 800 in3. The user solved for pressure P as P = kV-1.4, with k calculated as 100953.1751, leading to a final work value of W = 9.35 x 1011. The user initially questioned their calculations but later identified their error independently.

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  • Integral calculus fundamentals
  • Understanding of thermodynamic equations
  • Knowledge of pressure-volume relationships in steam engines
  • Familiarity with units of measurement in engineering (e.g., lbs/in2, in3)
NEXT STEPS
  • Study the application of the Ideal Gas Law in thermodynamics
  • Learn about the derivation and application of the work-energy principle
  • Explore numerical integration techniques for engineering problems
  • Investigate the performance characteristics of steam engines
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Mechanical engineers, thermodynamics students, and anyone involved in the analysis and optimization of steam engine performance will benefit from this discussion.

johnnyboy2005
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this is a question about a steam engine with the equation (sorry for lack of proper math language)

PV^1.4 = k (constant)


using the idea of integral from V1 to V2

ie...


the amount of work done is W=(int.V1 to V2) PdV

Where P1=160lbs/in^2
and V1 = 100 in^3...V2=800 in^3

solving for P we can find P=kV^(-1.4)...where k is 100953.1751

now i solved for in the integral

160*(100953.1751) *[ .4 V^.4] from 100 to 800 (for V)

i found W=9.35 * 10^11


Did i do this properly?
thanks for the help.
 
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it's okay...i figured out where i went wrong
 

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