Charlet's Law and Experiments

Introduction

• Follow-up to Boyle's Law, focusing on the V = T part of the ideal gas equation.
• Introduced by Jacques Charlet, a French physicist.
• Known for filling a hot air balloon with hydrogen gas and flying solo.

Charlet's Experiments

• Scenario: Heating gas in a closed container (e.g., a piston) under constant pressure.
  • As the gas is heated, its volume increases even though the number of particles remains constant.
• Volume increases proportionally to the increase in temperature.

Graphical Representation

• Plots showing volume expansion of different gases with temperature.
  • Example gases: Helium, Methane, Water Vapor, Hydrogen.
• Linear relationship depicted in Y-intercept form: ( y = mx + b )
  • ( y ) is volume ( V )
  • ( x ) is temperature ( T )

Observations from Graph

• Different gases have different slopes due to varying number of moles.
• Lines intercept at different points because gases liquefy at different temperatures (boiling points).
• Absolute zero: Extrapolated lines show all gases reach zero volume at -273.15°C (0 Kelvin).
  • Proof that -273.15°C is the lowest theoretical temperature (absolute zero).

Charlet's Law in Ideal Gas Equation

• Simplified equation: ( V = mT )
  • Removing ( b ) as Y-intercept is 0.
  • Re-arranged: ( \frac{V}{T} = m ) indicating constant volume/temperature ratio.
• Applicable under constant pressure and constant number of moles.

Example Problem

• Given: Initial conditions: 4.31 liters at 25°C.
• Required: Volume at 50°C assuming constant pressure.
• **Steps to Solve:"
  • Use ( V_1/T_1 = V_2/T_2 ) where temperature is in Kelvin.
  • Convert temperatures to Kelvin:
    • 25°C = 298K
    • 50°C = 323K
  • Solve for ( V_2 ):
    • Substitute values: ( V_2 = \frac{323 \times 4.31}{298} )
    • Result: ( V_2 = 4.67 \text{ liters} )

Conclusion

• Charlet's Law helps predict volume changes with temperature changes in a closed system under constant pressure.
• Reinforces understanding and application of the ideal gas equation in thermodynamics.