Lecture Notes: Thermal Physics - Ideal Gases Part 2

Introduction

• Revision of thermal physics, focusing on ideal gases.
• Part 2 of the series; for Part 1, refer to the provided link.

Key Concepts

Mole

• A mole is the amount of substance containing as many particles as there are atoms in 12 grams of carbon-12.
• Avogadro's number ( N_A = 6.02 \times 10^{23} ) particles per mole.

Molar Mass

• Allows calculation of the mass of one mole of a substance.
• Example: Molar mass of water is 18 g/mol.
• Calculation: ( \text{Number of moles} = \frac{\text{Mass}}{\text{Molar Mass}} ).

Number of Particles

• ( \text{Number of particles} = \text{Number of moles} \times N_A ).

Example Calculation

• 300g of water with molar mass 18 g/mol:
  • Number of moles = 16.67 moles.
  • Number of particles = ( 1.0 \times 10^{25} ).

Ideal Gases Assumptions

1. Large number of particles in random motion.
2. Particles occupy negligible volume.
3. Collisions are perfectly elastic.
4. Negligible forces between particles except during collisions.

Ideal Gas Law

• Equation 1: ( PV = nRT )
  • ( P ): Pressure, ( V ): Volume, ( n ): Moles, ( R ): Gas constant (8.31 J/mol·K), ( T ): Temperature in Kelvin.
• Equation 2: ( PV = NkT )
  • ( N ): Number of particles, ( k ): Boltzmann's constant (( 1.38 \times 10^{-23} )).

Relationship Between Constants

• Boltzmann's constant ( k = \frac{R}{N_A} ).

Laws and Experiments

Boyle’s Law

• At constant temperature, ( P ) is inversely proportional to ( V ).
• Experiment: Measure pressure against ( 1/V ) using a pressure gauge.

Pressure Temperature Law

• At constant volume, ( P ) is directly proportional to ( T ).
• Experiment: Use a sealed flask submerged in a water bath, measure ( P ) against ( T ).

Kinetic Model and Pressure

• Pressure defined as the sum of collision forces divided by area of the container.

Root Mean Square Speed (RMS)

• Calculate using squared speeds, mean, and then the square root.
• Important for equations relating pressure and mean squared speed.

Maxwell-Boltzmann Distribution

• Plots particles speed distribution:
  • Few have low/high speeds.
  • Most have moderate speeds.
• Effect of temperature: Higher temperature flattens and broadens the distribution curve.

Temperature and Kinetic Energy

• ( \text{Mean K.E.} = \frac{3}{2}kT ).
• Relationship derived by equating two forms of PV equations.

Practical Application

• Estimating molecular speeds at a given temperature using molar mass and Avogadro’s number.

Conclusion

• Comprehensive revision of ideal gas laws, kinetic theory, and related concepts in thermal physics.
• Thank you for attending, and stay tuned for next sessions.