How do I calculate work when both pressure and volume are changing?

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SUMMARY

The calculation of work done by a gas when both pressure and volume are changing is defined by the equation W = ∫ P(V) dV. This integral accounts for the variable nature of pressure as the volume changes, allowing for accurate work computation in thermodynamic processes. Understanding this concept is crucial for solving problems in physics and engineering where gas behavior is analyzed.

PREREQUISITES
  • Understanding of thermodynamic principles
  • Familiarity with calculus, specifically integration
  • Knowledge of gas laws and behavior
  • Experience with pressure-volume (P-V) diagrams
NEXT STEPS
  • Study the derivation of the work done by a gas in non-constant pressure scenarios
  • Learn about the First Law of Thermodynamics and its applications
  • Explore advanced topics in thermodynamics, such as isothermal and adiabatic processes
  • Investigate real-world applications of gas work calculations in engineering
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Students and professionals in physics and engineering fields, particularly those focusing on thermodynamics and fluid mechanics.

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i need help when trying to find the work done by a gas when the pressure and volume are BOTH changing. i know the ( W=P x (change in V) and how to solve problems when pressure is constant, but i don't know what to do when P and V both change.

please post an equation, thanks.
 
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Use: dW = P(V) dV or W = Integral [ P(v) dV ]
 

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