🔋College Physics I – Introduction Unit 15 – Thermodynamics

Key Concepts and Definitions

• Thermodynamics studies the relationships between heat, work, temperature, and energy
• System refers to the specific object or region under study
  • Open system can exchange both energy and matter with its surroundings
  • Closed system exchanges only energy with its surroundings, not matter
• Surroundings include everything outside the system
• State variables describe the current condition of a system (temperature, pressure, volume)
• Thermal equilibrium occurs when two systems have the same temperature and no net heat flows between them
• Thermal energy is the total kinetic and potential energy of the particles in a system
• Heat is the transfer of thermal energy between systems or a system and its surroundings

Laws of Thermodynamics

• Zeroth Law states that if two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other
• First Law states that energy cannot be created or destroyed, only converted from one form to another
  • Mathematically: $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is heat added, and $W$ is work done by the system
• Second Law states that the total entropy of an isolated system always increases over time
  • Entropy is a measure of the disorder or randomness of a system
• Third Law states that the entropy of a perfect crystal at absolute zero is zero
• The laws govern the behavior of energy in thermodynamic systems and set limits on efficiency

Temperature and Heat

• Temperature measures the average kinetic energy of particles in a system
  • Kinetic energy is the energy of motion
• Heat is the transfer of thermal energy from a hotter object to a cooler object
• Specific heat capacity is the amount of heat required to raise the temperature of one unit mass of a substance by one degree
  • Mathematically: $Q = mc\Delta T$, where $Q$ is heat, $m$ is mass, $c$ is specific heat capacity, and $\Delta T$ is the change in temperature
• Thermal expansion occurs when a substance expands due to an increase in temperature
• Phase changes (melting, freezing, vaporization, condensation) involve heat transfer without a change in temperature

Work and Energy in Thermodynamic Systems

• Work is the transfer of energy by a force acting through a distance
  • Mathematically: $W = Fd$, where $W$ is work, $F$ is force, and $d$ is distance
• In thermodynamics, work often involves a change in volume against an external pressure
  • Mathematically: $W = -P\Delta V$, where $W$ is work, $P$ is pressure, and $\Delta V$ is the change in volume
• Internal energy is the sum of the kinetic and potential energies of the particles in a system
• The change in internal energy is equal to the heat added minus the work done by the system (First Law)
• Heat and work are both forms of energy transfer between a system and its surroundings

Thermodynamic Processes

• Isothermal process occurs at constant temperature
  • Requires heat transfer between the system and surroundings to maintain constant temperature
• Adiabatic process occurs without any heat transfer between the system and surroundings
  • Often involves rapid compression or expansion
• Isobaric process occurs at constant pressure
• Isochoric (isovolumetric) process occurs at constant volume
• Cyclic process returns the system to its initial state after a series of state changes
  • The net change in internal energy for a cyclic process is zero

Heat Engines and Efficiency

• Heat engine converts thermal energy into mechanical work by cycling between a high-temperature reservoir and a low-temperature reservoir
  • Examples include internal combustion engines and steam turbines
• Thermal efficiency is the ratio of the useful work output to the heat input
  • Mathematically: $e = \frac{W}{Q_H}$, where $e$ is efficiency, $W$ is work output, and $Q_H$ is heat input from the high-temperature reservoir
• Carnot efficiency is the maximum theoretical efficiency of a heat engine operating between two temperatures
  • Mathematically: $e_{Carnot} = 1 - \frac{T_C}{T_H}$, where $T_C$ is the cold reservoir temperature and $T_H$ is the hot reservoir temperature
• The Second Law limits the efficiency of heat engines, as some heat must always be rejected to the low-temperature reservoir

Applications in Real-World Systems

• Refrigerators and heat pumps are reverse heat engines that move thermal energy from a cold reservoir to a hot reservoir
  • Coefficient of Performance (COP) measures the efficiency of these devices
• Power plants use heat engines to generate electricity from thermal energy (fossil fuels, nuclear reactions, geothermal sources)
• Automotive engines convert the chemical energy of fuel into mechanical work through a heat engine cycle (Otto cycle for gasoline, Diesel cycle for diesel)
• Thermodynamic principles are applied in HVAC (Heating, Ventilation, and Air Conditioning) systems to control indoor environments
• Phase change materials (PCMs) are used for thermal energy storage in applications such as solar energy systems and temperature regulation in buildings

Problem-Solving Strategies

• Identify the system and its surroundings
• Determine the initial and final states of the system
• Apply the relevant laws of thermodynamics (First Law for energy conservation, Second Law for efficiency and entropy)
• Use the appropriate equations for the specific process (isothermal, adiabatic, isobaric, isochoric)
  • Ideal gas law: $PV = nRT$
  • Work done by a gas: $W = -P\Delta V$
  • Heat transfer: $Q = mc\Delta T$
• Consider any energy transfers (heat and work) between the system and surroundings
• Analyze the efficiency of heat engines and reverse heat engines using the appropriate formulas
• Check units and ensure that the answer makes sense in the context of the problem