Thermal Physics Notes

Thermal Physics Overview

• Thermal physics encompasses the study of thermodynamics and gas laws.

Specific Heat Capacity

• Definition: The amount of heat required to raise the temperature of 1 kg of a substance by 1°C (or 1 K).
• Units: J/kg°C or J/kgK.
• Water vs. Iron:
  • Specific heat capacity of water: 4200 J/kg°C
  • Specific heat capacity of iron: 452 J/kg°C
• Implications:
  • Water requires significantly more energy to increase its temperature compared to iron, making iron heat up more quickly.
• Formula:
  • $c = \frac{Q}{m \theta}$
  • Where:
  • $c$ = specific heat capacity
  • $Q$ = heat supplied
  • $m$ = mass of the substance
  • $\theta$ = temperature change

Specific Latent Heat

• Definition: The amount of heat needed to change the phase of 1 kg of a substance at constant temperature without changing temperature (i.e., during melting or boiling).
• Units: J/kg.
• Formula:
  • $L = \frac{Q}{m}$
  • Where:
  • $L$ = specific latent heat
  • $Q$ = latent heat absorbed/released
  • $m$ = mass of the substance
• Types of Latent Heat:
  • Fusion: Heat required to convert solid to liquid (smaller than vaporization).
  • Vaporization: Heat required to convert liquid to gas.

Gas Laws

• Three primary gas laws: Boyle’s Law, Charles’s Law, and Pressure Law.
• Factors Affecting Gases:
  • Quantity (n in moles)
  • Temperature (T in Kelvin)
  • Pressure (P in Pascals)
  • Volume (V in cubic meters)

Boyle’s Law

• Statement: At constant temperature, the volume of a given mass of gas is inversely proportional to the absolute pressure.
• Equation:
  • $P<em>1V</em>1 = P<em>2V</em>2$
• Conclusion: If volume increases, pressure decreases (and vice-versa).

Charles’s Law

• Statement: At constant pressure, the volume of a given mass of gas is directly proportional to the absolute temperature.
• Example:
  • If a 30 cm³ balloon is heated from 27°C to 127°C, the final volume calculated:
  • Convert temperatures: 27 + 273 = 300 K, 127 + 273 = 400 K
  • Calculate final volume: V1 / T1 = V2 / T2

Pressure Law (Gay-Lussac’s Law)

• Statement: At constant volume, the pressure of a given mass of gas is directly proportional to the absolute temperature.
• Example: Using pressures and temperatures of air in a car tire to find final temperature after a long journey.

Combined Gas Law

• Combines Boyle’s, Charles’, and Gay-Lussac’s Laws:
  • $\frac{P<em>1V</em>1}{T<em>1} = \frac{P</em>2V<em>2}{T</em>2}$

Ideal Gas Law

• Describes the behavior of ideal gases:
  • $PV = nRT$
• Variables:
  • $P$ = Pressure
  • $V$ = Volume
  • $n$ = Moles of gas
  • $T$ = Temperature in Kelvin
  • $R$ = Universal Gas Constant (8.31 J/(mol·K))

Kinetic Molecular Theory of Gases

• Key Points:
  1. Gas molecules are separated by distances much greater than their size.
  2. They are in constant random motion and collide elastically.
  3. No attractive or repulsive forces between molecules.
  4. Average kinetic energy is proportional to temperature in Kelvin:
  • $KE = \frac{1}{2} mu^2$
• Summary: The theory explains the behavior of ideal gases, focusing on their motion and energy related to temperature.