Lecture on Boyle's Law

Introduction

• Robert Boyle: 17th-century Irish scientist
• Known for experiments with gases leading to Boyle's Law
• Boyle's Law predates the ideal gas equation

Boyle's Experiment

• Used a J-tube setup to experiment with gases
• Trapped gas in the tube using mercury
  • Mercury is dense and traps gas effectively
• Open side exposed to atmospheric pressure

Observations From the Experiment

• Initial mercury level was equal on both sides
• Adding mercury created a height difference indicating pressure changes
• The trapped gas pressure becomes greater than atmospheric pressure
• Pressure calculation: Gas pressure = Atmospheric pressure + Fluid pressure difference

Data Collection

• Boyle measured volume in cubic inches and pressure in inches of mercury
• Recorded data:
  • 117.5 cubic inches, 12 inches of mercury
  • 87.2 cubic inches, 16 inches of mercury
  • 70.7 cubic inches, 20 inches of mercury
  • 58.8 cubic inches, 24 inches of mercury
  • 44.2 cubic inches, 32 inches of mercury
  • 35.3 cubic inches, 40 inches of mercury
  • 29.1 cubic inches, 48 inches of mercury

Graph Analysis

• Plotted pressure as a function of volume
• Graph was a hyperbola indicating an inverse relationship
• As volume halved, pressure doubled
• Re-plotting volume vs. inverse of pressure gave a straight line

Mathematical Representation

• Equation from the graph: V = k * (1/P)
  • PV = k (constant)
  • Matches the ideal gas equation

Application of Boyle's Law

• If moles and temperature of a gas are constant, initial PV = final PV
• Example problem:
  • Initial conditions: 1.25 liters, 0.872 atmospheres
  • Final volume: 1.5 liters
  • Final pressure: 0.727 atmospheres

Conclusion

• Boyle's Law: pressure and volume of a gas are inversely proportional
• Useful for predicting behavior of gases under constant temperature and moles