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    • Thermodynamics >
      • Thermochemistry Worksheet + Answers
      • First Law of Thermodynamics
      • Pressure-Volume Work
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      • Enthalpy of Formation
      • Heat Capacity
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      • Redox Reactions
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      • Galvanic Cells
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      • Introduction
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      • Rate Laws
      • Zero-Order Reactions
      • First-Order Reactions
      • Second-Order Reactions
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      • Arrhenius Equation
      • How Long will it Take to Decay?
      • What Order is this Reaction?
      • Find the Rate Constant
      • Find the Activation Energy
    • Gases >
      • Pressure, Volume, Temperature
      • Ideal Gas Law
      • Density of Gases
      • Ideal Gas Law and Changes in P, V, T
      • Kinetic Molecular Theory
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      • Writing Equilibrium Expressions
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      • Acids and Bases Worksheet + Answers
      • Arrhenius vs Bronsted-Lowry vs Lewis Acids
      • Solve Titration Questions
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      • Phase Diagrams
      • Phase Changes
      • Intermolecular Forces
      • Effects of Intermolecular Forces
      • Ranking by Boiling/Melting Point
      • Clausius-Clapeyron Equation
      • Heating Curves
    • Solids >
      • Ionic/Metallic/Covalent
      • Symmetry of Solids
      • Simple Cubic, fcc and bcc
      • How to Find Edge Length
    • Organic Reactions >
      • Br2 + Alkene (Adding across a double bond)
      • HCl + Alkene (Adding across a double bond)
      • Reaction of OH with Alkyl Halide
      • What is Regioselectivity?
    • Moles and Mass >
      • Average Atomic Mass
      • Solve for Isotopic Abundance
      • Limiting Reagents
      • Percent Yield
      • Actual Yield and Percentage Yield
      • Percent Composition
    • Atomic Structure >
      • What's in an Atom?
      • Quantum Numbers
      • Pauli, Aufbau, Hund
      • Light: E h ν λ
      • Energy Levels of Hydrogen
      • Energy Levels of Non-Hydrogen Atoms
    • Organic Naming >
      • Naming Organic Molecules
      • How to Name Amines
      • How to Name Amides
  • Privacy Policy
  • Lewis Structures

Pressure-Volume Work


When a gas is compressed, work is obviously being done TO the system (so ΔW is positive). The formula for how much work is done is:
Picture
Pext is the external pressure ... the amount of pressure that the surroundings are applying to the system.

ΔV is the change in volume (in Litres) that the system experiences.

Do NOT forget the negative sign. It is needed so that a COMPRESSION (decrease in volume) corresponds to work being done TO the system.

It is also important to remember that 1 J = 1 L atm. If you put Pext in atm, and ΔV in Litres, then your answer will be in Joules.

Sample Question

Q: How much work is done on a balloon that is compressed from 6 L to half its original volume at atmospheric pressure?

A: Well:
  • Convert pressure from atm to kPa, so Pext = 101.325 kPa
    ΔV = Vfinal - Vinitial = 3 L - 6 L = -3 L.
  • This may seem obvious, since the balloon obviously loses 3 L of volume.
  • So, ΔW = -Pext(ΔV) = -(101.3 kPa)(-3 L) = 304 L kPa = 304 J

304 J of work is done to the balloon.

Shout-out to [a student, name withheld pending permission] from Arizona State for catching an error I made here earlier!  Corrected March 11, 2013.
Created by Nathan Oldridge (aka ChemistNATE).  All lessons here are Public Domain.