Combined Gas Law Lecture Notes

Introduction

• Topic: Combined Gas Law (Characteristic Gas Equation)
• Importance: Relates pressure, volume, and temperature simultaneously.

Key Concepts

• Boyle's Law: At constant temperature, pressure and volume are inversely proportional.
• Charles' Law: At constant pressure, volume and temperature are directly proportional.

Deriving the Combined Gas Law

• Process Overview:
  • Analyze a gas expanding from state 1 to state 2 (Boyle's Law).
  • Then from state 2 to state 3 (Charles' Law).

Process 1-2 (Boyle's Law)

• Plotting on Pressure-Volume (PV) Diagram:
  • Pressure (P) on y-axis, Volume (V) on x-axis.
  • State 1: P1, V1.
  • State 2: P2, V2.
  • Relationship: P1V1 = P2V2
  • Equation 1: V2 = (P1V1) / P2

Process 2-3 (Charles' Law)

• State 2: T2 = T1 (constant temperature).
• Apply Charles' Law:
  • V2/T2 = V3/T3
  • Equation 2: V2/T1 = V3/T3
• Substitute V2 from Equation 1:
  • P1V1/T1 = P2V3/T3

Generalization

• Each state relation can be generalized: PV/T = constant.
• This constant is the Characteristic Gas Constant (R).
• Equation 3: PV = MRT
  • For 1 kg of gas: R is specific for each gas.

Important Equations

• Equation 4: PV/T = mR
• Equation 5: PV = MRT (Characteristic Gas Equation)

Characteristic Gas Constant (R)

• R value for air: 0.287 kJ/kg·K
• Universal Gas Constant (Ru): 8.314 kJ/kg·mole·K
  • Ru = m * R (constant for all gases)*

Conclusion

• Remember the values for R and Ru for numerical problems.
• Engage with the content (like the video for appreciation)

• Note: Review each equation and its significance in solving gas law problems.