Unit 2: Thermodynamics

📚Study Guide: Thermodynamics

Unit 2: Thermodynamics

Thermodynamics is the study of heat, temperature, energy, and the conversion of heat into work. In AP Physics 2, you begin by distinguishing temperature—a measure of the average kinetic energy of particles in a substance—from heat, which is the transfer of thermal energy due to a temperature difference. You will learn about thermal expansion, where solids and liquids change dimensions as temperature changes, characterized by coefficients of linear and volume expansion. The ideal gas law, PV = nRT, forms the backbone of gas thermodynamics, relating pressure, volume, temperature, and the amount of gas. You must understand the kinetic theory of gases, which connects macroscopic pressure and temperature to the microscopic motion of molecules. For a monatomic ideal gas, the average translational kinetic energy per molecule is (3/2)kBT, and the internal energy U = (3/2)nRT depends only on temperature. The First Law of Thermodynamics, ΔU = Q − W, is essentially energy conservation for thermal systems: the change in internal energy equals the heat added to the system minus the work done by the system. Be careful with sign conventions; in physics, W represents work done by the gas on its surroundings. You will analyze four special thermodynamic processes on PV diagrams: isothermal (constant temperature, ΔU = 0), isochoric (constant volume, W = 0), isobaric (constant pressure, W = PΔV), and adiabatic (no heat transfer, Q = 0). The area under a curve on a PV diagram always represents the work done by the gas. Heat engines, which convert heat into work, operate in cycles on PV diagrams and are governed by the Second Law of Thermodynamics: no engine can be 100% efficient, and entropy—a measure of disorder—always increases for irreversible processes in an isolated system. The maximum possible efficiency is that of a Carnot engine: e = 1 − Tc/Th. On the AP Exam, thermodynamics questions frequently require you to interpret PV diagrams, calculate work as an area, apply the First Law, and compare the efficiencies of different cycles. A strong conceptual grasp of entropy and the irreversibility of natural processes separates top scorers from average ones.

Key Concepts

• Temperature vs. Heat: Temperature is a measure of average kinetic energy. Heat is energy transferred between systems due to a temperature difference.
• Thermal Expansion: Materials expand when heated. Linear expansion: ΔL = αL₀ΔT. Volume expansion: ΔV = βV₀ΔT.
• Ideal Gas Law: PV = nRT relates the state variables of an ideal gas. You can also write it as PV = NkBT using the number of molecules.
• Kinetic Theory: Pressure arises from molecular collisions. Average KE per molecule = (3/2)kBT. Internal energy of monatomic gas U = (3/2)nRT.
• First Law of Thermodynamics: ΔU = Q − W. Q is heat added to system; W is work done by system. This is conservation of energy.
• PV Diagram Processes: Isothermal (T constant), isochoric (V constant), isobaric (P constant), adiabatic (Q = 0). Work is the area under the curve.
• Second Law and Entropy: Heat flows spontaneously from hot to cold. Entropy of an isolated system never decreases. Real processes are irreversible.

Vocabulary

• Thermal Equilibrium: The state in which two objects in contact have the same temperature and no net heat flows between them.
• Internal Energy (U): The total microscopic kinetic and potential energy of the particles in a system.
• Molar Specific Heat: The amount of heat required to raise the temperature of one mole of a substance by one kelvin.
• Adiabatic: A process in which no heat is exchanged with the surroundings (Q = 0).
• Isothermal: A process that occurs at constant temperature (ΔU = 0 for ideal gas).
• Isochoric: A process at constant volume (W = 0).
• Entropy: A measure of the disorder or number of microscopic configurations of a system.
• Heat Engine: A device that converts thermal energy into mechanical work by operating in a cycle.

Essential Formulas

• ΔL = α * L0 * ΔT
• P*V = n*R*T (ideal gas law)
• KE_avg = (3/2) * kB * T
• U = (3/2) * n * R * T (monatomic ideal gas)
• ΔU = Q - W (First Law)
• W = ∫ P dV = area under PV curve
• e = 1 - Qc / Qh = 1 - Tc / Th (Carnot efficiency)
• e = W / Qh (general efficiency)

Common Mistakes

• Confusing Heat and Temperature: Heat is energy in transit; temperature is a state variable. Adding heat does not always raise temperature (e.g., phase changes, isothermal expansion).
• Forgetting Work Is Area Under PV Curve: For irregular paths, you must integrate or estimate the area. Do not assume W = PΔV unless pressure is constant.
• Using Wrong Sign Convention for W: In AP Physics, W is work done BY the gas. If the gas is compressed, work done BY the gas is negative (work is done ON the gas).
• Assuming 100% Efficiency Is Possible: The Second Law forbids perfect heat engines. Even reversible engines cannot exceed Carnot efficiency.

AP Exam Strategies

• Always Identify the Process Type First: Before writing any equation, determine if the process is isothermal, isochoric, isobaric, or adiabatic. This tells you which variables are zero or constant.
• Draw the PV Diagram: Sketch the path on a PV diagram. Label initial and final states. The area under the path gives the work done by the gas.
• Use the First Law as an Accounting Equation: Write ΔU = Q − W and fill in what you know. For an ideal gas, ΔU depends only on ΔT.
• Remember Isothermal Means ΔU = 0 for Ideal Gas: Therefore Q = W. Adiabatic means Q = 0, so ΔU = −W.

Real-World Applications

• Internal Combustion Engines: Automobile engines use cycles of compression, combustion, expansion, and exhaust to convert heat from fuel into mechanical work.
• Refrigerators: These are heat engines operating in reverse, using work to move heat from a cold reservoir to a hot reservoir.
• Thermal Expansion in Bridges: Expansion joints allow bridges to expand and contract with temperature changes without structural damage.