🧲AP Physics 2 (2025) Unit 9 – Thermodynamics

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, work, temperature, and energy
• System refers to the specific part of the universe under study (gas in a piston)
• Surroundings include everything external to the system
• Boundary separates the system from its surroundings and can be fixed or movable (piston)
• State variables describe the current condition of a system (temperature, pressure, volume)
  • State variables depend only on the current state, not on how the system reached that state
• Process describes the path or series of states through which a system passes (isothermal, adiabatic)
• Thermal equilibrium achieved when two systems have the same temperature and no heat flows between them
• Zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other

Laws of Thermodynamics

• First law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another
  • Mathematically expressed as $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is heat added to the system, and $W$ is work done by the system
• Second law of thermodynamics states that the total entropy of an isolated system always increases over time
  • Entropy is a measure of disorder or randomness in a system
  • Heat flows spontaneously from a hot object to a cold object, not the other way around
• Third law of thermodynamics states that the entropy of a perfect crystal at absolute zero is zero
  • Absolute zero (0 K or -273.15°C) is the lowest possible temperature, where all molecular motion stops
• Zeroth law of thermodynamics defines thermal equilibrium and provides the basis for temperature measurement

Thermal Properties of Matter

• Heat capacity measures the amount of heat required to raise the temperature of a substance by one degree
  • Specific heat capacity ($c$) is the heat capacity per unit mass (J/kg·K)
  • Molar heat capacity is the heat capacity per mole of a substance (J/mol·K)
• Thermal expansion occurs when a substance expands or contracts due to temperature changes
  • Linear thermal expansion describes length changes in one dimension
  • Volumetric thermal expansion describes volume changes in three dimensions
• Phase transitions occur when a substance changes from one state of matter to another (solid, liquid, gas)
  • Latent heat is the energy required for a substance to change phase without a change in temperature
  • Latent heat of fusion is the energy required to change a substance from solid to liquid (or vice versa)
  • Latent heat of vaporization is the energy required to change a substance from liquid to gas (or vice versa)

Heat Transfer Mechanisms

• Conduction is the transfer of heat through direct contact between particles of matter
  • Thermal conductivity ($k$) measures a material's ability to conduct heat (W/m·K)
  • Fourier's law of thermal conduction describes the rate of heat transfer through a material
• Convection is the transfer of heat by the movement of fluids (liquids or gases)
  • Natural convection occurs due to density differences caused by temperature variations
  • Forced convection occurs when an external force, such as a fan or pump, moves the fluid
• Radiation is the transfer of heat through electromagnetic waves
  • All objects emit thermal radiation based on their temperature
  • Stefan-Boltzmann law describes the power radiated by an object as proportional to its temperature to the fourth power
• Insulation reduces heat transfer by slowing down conduction, convection, or radiation
  • Materials with low thermal conductivity (foam, fiberglass) are good insulators

Thermodynamic Processes

• Isothermal process occurs at constant temperature
  • Ideal gas law ($PV = nRT$) applies, with $T$ remaining constant
• Isobaric process occurs at constant pressure
  • Ideal gas law applies, with $P$ remaining constant
• Isochoric (isovolumetric) process occurs at constant volume
  • Ideal gas law applies, with $V$ remaining constant
• Adiabatic process occurs without heat transfer between the system and its surroundings
  • Pressure and volume are related by the equation $PV^\gamma = \text{constant}$, where $\gamma$ is the ratio of specific heats
• Cyclic process occurs when a system returns to its initial state after undergoing a series of thermodynamic processes
  • Heat engines (internal combustion engines) and refrigerators operate on cyclic processes

Entropy and the Second Law

• Entropy ($S$) is a measure of the disorder or randomness in a system
  • Mathematically, entropy change is defined as $\Delta S = \int \frac{dQ}{T}$, where $dQ$ is the heat added reversibly and $T$ is the absolute temperature
• Second law of thermodynamics states that the total entropy of an isolated system always increases over time
  • Spontaneous processes occur with an increase in entropy (gas expanding into a vacuum)
  • Reversible processes occur with no change in entropy (idealized, infinitely slow processes)
  • Irreversible processes occur with an increase in entropy (heat transfer, friction)
• Entropy and the second law explain why certain processes are impossible (perpetual motion machines)
  • Heat cannot spontaneously flow from a cold object to a hot object
  • Work cannot be completely converted into heat without some heat being lost to the surroundings

Applications in Real-World Systems

• Heat engines convert thermal energy into mechanical work (internal combustion engines, steam turbines)
  • Efficiency of a heat engine depends on the temperature difference between the hot and cold reservoirs
  • Carnot cycle represents the most efficient heat engine operating between two temperatures
• Refrigerators and heat pumps move thermal energy from a cold reservoir to a hot reservoir
  • Coefficient of performance (COP) measures the efficiency of refrigerators and heat pumps
  • Reverse Carnot cycle represents the most efficient refrigerator or heat pump operating between two temperatures
• Thermodynamic principles apply to various systems (power plants, HVAC systems, biological systems)
  • Efficiency and sustainability can be improved by understanding and applying thermodynamic concepts
  • Energy conservation and waste heat recovery can reduce energy consumption and environmental impact

Problem-Solving Strategies

• Identify the system and its surroundings
  • Define the boundaries and interactions between the system and surroundings
• Determine the initial and final states of the system
  • Identify the state variables (temperature, pressure, volume) at the beginning and end of the process
• Apply the relevant thermodynamic laws and principles
  • Use the first law of thermodynamics to analyze energy conservation and heat transfer
  • Use the second law of thermodynamics to determine the direction of spontaneous processes and entropy changes
• Use the appropriate equations and relationships for the specific process
  • Ideal gas law ($PV = nRT$) for processes involving ideal gases
  • Specific heat capacity ($Q = mc\Delta T$) for heat transfer problems
  • Latent heat equations ($Q = mL$) for phase transition problems
• Pay attention to units and convert them as needed
  • Use SI units (Joules, Kelvin, Pascals) for consistency
  • Convert between units using appropriate conversion factors (1 cal = 4.184 J)
• Check your results for reasonableness and consistency with thermodynamic principles
  • Ensure that energy is conserved and entropy increases for spontaneous processes
  • Verify that your answer makes sense in the context of the problem and real-world applications