🧲AP Physics 2 Unit 2 – Thermodynamics

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, work, temperature, and energy
• Internal energy represents the total kinetic and potential energy of a system's particles
• Heat is the transfer of thermal energy between systems or within a system
• Temperature measures the average kinetic energy of particles in a substance
• Entropy quantifies the amount of disorder or randomness in a system
• Thermal equilibrium occurs when two systems in contact have the same temperature and no net heat transfer
• Specific heat capacity is the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius
  • Varies depending on the material (water, aluminum, copper)

Laws of Thermodynamics

• The zeroth law establishes the concept of thermal equilibrium and temperature
• The first law 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
• The second law introduces the concept of entropy and states that the total entropy of an isolated system always increases over time
  • Implies that heat flows naturally from a hotter object to a colder object until thermal equilibrium is reached
• The third law states that the entropy of a perfect crystal at absolute zero is zero
  • Absolute zero (0 Kelvin or -273.15°C) is the lowest possible temperature, where particles have minimal kinetic energy

Heat Transfer Mechanisms

• Conduction is the transfer of heat through direct contact between particles of a substance
  • Occurs in solids, liquids, and gases
  • Rate of conduction depends on the material's thermal conductivity (metals, insulators)
• Convection is the transfer of heat by the movement of fluids or gases
  • Involves the bulk motion of molecules within fluids (liquids and gases)
  • Examples include hot air rising and the formation of ocean currents
• Radiation is the transfer of heat through electromagnetic waves
  • Does not require a medium and can occur in a vacuum
  • Emitted by all objects with a temperature above absolute zero (Sun, Earth, human body)
• Insulation slows down heat transfer by reducing conduction, convection, or radiation
  • Materials with low thermal conductivity (fiberglass, foam, air gaps) are effective insulators

Thermodynamic Systems and Processes

• An open system exchanges both matter and energy with its surroundings (boiling water in an uncovered pot)
• A closed system exchanges energy but not matter with its surroundings (a sealed container with a movable piston)
• An isolated system does not exchange matter or energy with its surroundings (a perfectly insulated container)
• Isothermal processes occur at constant temperature, with heat transfer balanced by work done (slow compression or expansion of a gas)
• Adiabatic processes occur without heat transfer between the system and its surroundings (rapid compression or expansion of a gas)
• Isobaric processes occur at constant pressure (heating a gas in a container with a movable piston)
• Isochoric (isovolumetric) processes occur at constant volume (heating a gas in a rigid container)

Work and Energy in Thermodynamics

• Work is the energy transferred by a force acting through a distance
  • In thermodynamics, work often involves the expansion or compression of a gas (a piston moving in a cylinder)
• The work done by a gas during expansion is positive, while work done on a gas during compression is negative
• The first law of thermodynamics relates changes in internal energy to heat and work ($\Delta U = Q - W$)
• Heat engines convert thermal energy into mechanical work by exploiting temperature differences
  • Examples include internal combustion engines and steam turbines
• Efficiency is the ratio of useful work output to total energy input
  • Limited by the second law of thermodynamics and the impossibility of a 100% efficient heat engine

Gas Laws and Ideal Gas Behavior

• The ideal gas law relates pressure, volume, temperature, and the number of moles of a gas: $PV = nRT$
  • $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the universal gas constant, and $T$ is the absolute temperature
• Boyle's law states that the pressure and volume of a gas are inversely proportional at constant temperature ($P_1V_1 = P_2V_2$)
• Charles's law states that the volume and temperature of a gas are directly proportional at constant pressure ($\frac{V_1}{T_1} = \frac{V_2}{T_2}$)
• Gay-Lussac's law states that the pressure and temperature of a gas are directly proportional at constant volume ($\frac{P_1}{T_1} = \frac{P_2}{T_2}$)
• The combined gas law relates changes in pressure, volume, and temperature ($\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$)
• Kinetic molecular theory explains the behavior of gases based on the motion and interactions of their particles
  • Assumes particles are in constant random motion, colliding elastically with each other and the container walls

Applications and Real-World Examples

• Heat engines, such as internal combustion engines and steam turbines, apply thermodynamic principles to generate power (cars, power plants)
• Refrigerators and heat pumps use the principles of heat transfer and the second law of thermodynamics to move heat from a colder region to a hotter region
• Insulation in buildings and clothing helps maintain comfortable temperatures by reducing heat transfer
• Weather patterns and climate are influenced by heat transfer mechanisms (convection in the atmosphere and oceans)
• Thermodynamics plays a crucial role in designing and optimizing various industrial processes (chemical reactions, manufacturing)
• Biological systems, such as the human body, rely on thermodynamic principles to maintain homeostasis and perform essential functions (metabolism, thermoregulation)

Problem-Solving Strategies

• Identify the system and its boundaries (open, closed, or isolated)
• Determine the initial and final states of the system (pressure, volume, temperature)
• Apply the relevant laws and equations (first law of thermodynamics, ideal gas law, gas laws)
  • Use the given information to solve for the unknown variable
• Consider the assumptions and limitations of the models used (ideal gas behavior, adiabatic processes)
• Analyze the direction of heat transfer and the sign of work done (positive for expansion, negative for compression)
• Use dimensional analysis to ensure the units of the solution are correct
• Check the reasonableness of the answer based on the problem's context and physical intuition