Temperature measures how hot or cold something is, based on how fast its particles move. The faster they move, the hotter it is. This connects to thermal energy, which is the total energy of all particles in a substance.

Different temperature scales exist, like Celsius, Fahrenheit, and Kelvin. We can convert between them using simple equations. Kelvin is special because it starts at absolute zero, the coldest possible temperature where particles stop moving.

Temperature and Thermal Energy

Temperature and particle kinetic energy

• Temperature measures the average kinetic energy of particles in a substance
  • Higher temperatures indicate particles have higher average kinetic energy (faster motion)
  • Lower temperatures indicate particles have lower average kinetic energy (slower motion)
• Particles in a substance constantly move and collide with each other
  • Increasing temperature causes particles to move faster and collide more frequently with greater force (boiling water)
  • Decreasing temperature causes particles to move slower and collide less frequently with less force (freezing water)
• The relationship between temperature and average kinetic energy is linear
  • Doubling the temperature doubles the particles' average kinetic energy (heating a gas)
  • Halving the temperature halves the particles' average kinetic energy (cooling a gas)
• Temperature gradients can form when there are differences in temperature within a system or between systems

Conversion of temperature scales

• Celsius (℃) and Kelvin (K) scales are related by a constant offset
  • To convert Celsius to Kelvin: $K = ℃ + 273.15$
  • To convert Kelvin to Celsius: $℃ = K - 273.15$
• Fahrenheit (℉) and Celsius scales are related by a linear equation
  • To convert Celsius to Fahrenheit: $℉ = (℃ × 9/5) + 32$
  • To convert Fahrenheit to Celsius: $℃ = (℉ - 32) × 5/9$
• Fahrenheit and Kelvin scales can be converted by combining the above equations
  • To convert Fahrenheit to Kelvin: $K = (℉ - 32) × 5/9 + 273.15$
  • To convert Kelvin to Fahrenheit: $℉ = (K - 273.15) × 9/5 + 32$

Absolute zero on Kelvin scale

• Absolute zero is the lowest possible temperature where particles have no kinetic energy
  • Defined as 0 K, -273.15 ℃, or -459.67 ℉
  • At absolute zero, particles theoretically have no vibrational, rotational, or translational motion (helium at extremely low temperatures)
• The Kelvin scale is an absolute temperature scale with its zero point at absolute zero
  • Kelvin temperatures are always positive starting from absolute zero (0 K)
  • Kelvin scale directly relates to particles' average kinetic energy (ideal gas law)
• Reaching absolute zero is practically impossible due to the laws of thermodynamics
  • Removing the remaining heat from a substance becomes increasingly difficult as temperature approaches absolute zero (cooling to near 0 K)
  • The third law of thermodynamics states reaching absolute zero would require infinite steps and energy (Nernst heat theorem)

Heat and Energy Transfer

• Heat transfer occurs when there is a temperature difference between systems
• Thermal equilibrium is reached when two systems have the same temperature and no net heat transfer occurs
• The specific heat capacity of a material determines how much energy is required to change its temperature
• Latent heat is the energy absorbed or released during a phase change without changing temperature
• Thermodynamics studies the relationships between heat, work, temperature, and energy
  • The concept of entropy is central to the second law of thermodynamics, describing the disorder in a system