thermodynamics

Thermal Energy

• Definition: Thermal energy is the total kinetic and potential energy of particles in an object.
• Key Concept: It is closely related to temperature and how energy is transferred.

Temperature

• Definition: Temperature is the measure of average kinetic energy of particles.
  • Low kinetic energy = low temperature
  • High kinetic energy = high temperature
• Measurement Scales:
  • Celsius (°C)
  • Freezing point of water: 0°C
  • Boiling point of water: 100°C
  • Fahrenheit (°F)
  • Freezing point of water: 32°F
  • Boiling point of water: 212°F
  • Kelvin (K)
  • Freezing point of water: 273.15 K
  • Boiling point of water: 373.15 K
  • Absolute zero is defined as 0 K (the lowest possible temperature).
• Conversion Formulas:
  • Celsius to Fahrenheit: $T(°F) = \frac{9}{5} T(°C) + 32$
  • Fahrenheit to Celsius: $T(°C) = \frac{5(T(°F) - 32)}{9}$
  • Celsius to Kelvin: $T(K) = T(°C) + 273.15$
  • Kelvin to Celsius: $T(°C) = T(K) - 273.15$
  • Fahrenheit to Kelvin: $T(K) = \frac{5(T(°F) - 32)}{9} + 273.15$
  • Kelvin to Fahrenheit: $T(°F) = \frac{9}{5}(T(K) - 273.15) + 32$

Ideal Gas Law

• Equation: $PV = nRT$
  • P = Pressure (atm)
  • V = Volume (liters)
  • n = number of moles
  • R = ideal gas constant
  • T = Temperature (K)
• Energy of an Ideal Gas: $U = \frac{2}{3} nRT$

Heat Transfer

• Definition: Heat (Q) is the spontaneous transfer of energy due to temperature differences.
• Thermal Equilibrium: Heat flows from hot to cold until temperatures equalize.
• Key Principle: Heat transfer depends on the size, composition, and specific heat of the object.
  • Specific Heat Formula: $Q = mc\Delta T$
  • m = mass
  • c = specific heat of the substance
  • \Delta T = change in temperature
• Specific Heat Values (example):
  • Water: 4186 J/kg°C
  • Aluminum: 900 J/kg°C

Phase Changes

• Latent Heat: Heat required for a substance to change phase without changing temperature.
  • Latent Heat of Fusion: $Q = mL_f$ (solid to liquid)
  • Latent Heat of Vaporization: $Q = mL_v$ (liquid to gas)

Laws of Thermodynamics

• Zeroth Law: If two systems are in thermal equilibrium with a third system, they are in equilibrium with each other.
• First Law (Conservation of Energy): The change in internal energy, $\Delta U$, is equal to heat added to the system, $Q$, minus work done by the system, $W$:
  • $\Delta U = Q - W$
  • Sign conventions: +Q (heat absorbed), -Q (heat released), +W (work done by system), -W (work done on system).

Thermodynamic Processes

1. Isobaric: Constant pressure (work done by gas).
2. Isochoric: Constant volume (no work done).
3. Isothermal: Constant temperature.
4. Adiabatic: No heat exchange with the surroundings.

Second and Third Law of Thermodynamics

• Second Law: Heat transfer occurs spontaneously from high to low temperature, not the reverse.
• Third Law: As temperature approaches absolute zero, the entropy of a perfect crystal approaches zero.