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3.5 - Pressure & Volume (PV = Constant)

Sep 1, 2025

Overview

This lecture explains how gas pressure relates to volume, describes the inverse relationship using a key equation, and demonstrates how to solve typical gas law calculation problems.

Pressure and Volume Relationship in Gases

  • Pressure in gases is caused by particles colliding with container walls.
  • Increasing temperature, increasing the number of particles, or decreasing volume increases gas pressure.
  • Pressure (P) and volume (V) are inversely related: as volume increases, pressure decreases, and vice versa.
  • For a fixed amount of gas at constant temperature, the product of pressure and volume is constant (PV = constant).

Using PV = Constant in Calculations

  • If the gas changes from one state to another with constant temperature and mass, PV before equals PV after: ( P_1V_1 = P_2V_2 ).
  • To solve for unknowns, plug in values you know and rearrange the equation as needed.

Example Problems

  • Example 1: 1.5 m³ of gas at 100 Pa is compressed to 0.3 m³. Using PV = constant, the new pressure is 500 Pa.
  • Alternative approach: Use ( P_1V_1 = P_2V_2 ) directly to solve for unknown pressures or volumes.
  • Example 2: 1800 L of air at 101 kPa is compressed into a 12 L cylinder; the resulting pressure is 15,150 kPa.

Key Terms & Definitions

  • Pressure (P) — The force exerted by gas particles colliding with container walls, measured in Pascals (Pa) or kilopascals (kPa).
  • Volume (V) — The space occupied by the gas, measured in cubic meters (m³) or liters (L).
  • PV = constant — The equation showing that, for constant temperature and mass, pressure and volume multiply to a constant value.
  • Inverse Relationship — As one variable increases, the other decreases.

Action Items / Next Steps

  • Practice solving gas law problems using ( P_1V_1 = P_2V_2 ).
  • Review units for pressure and volume in calculations.