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Physics 2 Unit 1: Thermodynamics

Thermodynamics relates heat, work and internal energy, and the second law limits how efficiently heat can be turned into work.

Covers: Temperature and the ideal gas law, kinetic theory, heat transfer, internal energy, the first law, PV diagrams and thermodynamic processes, entropy and the second law, heat engines

Study guide

Temperature measures the average kinetic energy of particles; in kelvins, T(K) = T(°C) + 273. The ideal gas law is PV = nRT = NkBT. Kinetic theory says the average translational kinetic energy of a gas molecule is (3/2)kBT, so heavier molecules move more slowly at the same temperature, and the root-mean-square speed is √(3kBT/m). Thermal equilibrium means no net heat flows between objects at the same temperature (the zeroth law). Heat (Q) is energy transferred because of a temperature difference, by conduction (contact), convection (fluid movement) and radiation (electromagnetic waves). The rate of conduction through a material is Q/Δt = kAΔT/L. Specific heat relates heat to temperature change (Q = mcΔT), and latent heat applies during phase changes (Q = mL).

The first law of thermodynamics is conservation of energy: ΔU = Q + W, where W is work done on the gas (in the AP convention). For a gas, work done on it is W = −PΔV, the negative area under a PV diagram curve. In an isobaric process pressure is constant; in an isochoric (isovolumetric) process volume is constant and W = 0; in an isothermal process temperature is constant, so ΔU = 0 and Q = −W; and in an adiabatic process no heat flows, so ΔU = W. In a cyclic process, ΔU = 0 for a full cycle, and the net work equals the area enclosed by the cycle. The internal energy of an ideal monatomic gas is U = (3/2)nRT.

The second law says heat flows naturally from hot to cold, and the total entropy of an isolated system never decreases. A heat engine takes in heat from a hot reservoir, does work and releases heat to a cold reservoir; its efficiency is e = W/QH = 1 − QC/QH. No engine can be 100% efficient. The maximum possible efficiency is the Carnot efficiency, e = 1 − TC/TH (in kelvins). Refrigerators and heat pumps use work to move heat from cold to hot.

The speeds of gas particles follow a Maxwell–Boltzmann distribution. At a higher temperature the peak moves to higher speeds and the curve becomes lower and wider, while the area under it (the number of particles) stays the same. Pressure is force per unit area (P = F/A), and the force from a gas acts perpendicular to every surface it touches. For a piston of mass M at rest, the gas pushes up with P_gas·A, which balances the atmosphere's P_atm·A plus the weight Mg, so P_gas = P_atm + Mg/A.

On a PV diagram, an isochoric process is a vertical line and an isobaric process is a horizontal line. An isothermal process for an ideal gas is a curve where PV stays constant (P is inversely proportional to V), and an adiabatic curve is steeper than an isotherm. Arrows show the direction of the process, and moving to the right means the gas does positive work. Entropy measures how spread out energy is in a system, and it is a state function. The total entropy of an isolated system stays constant only for reversible processes and increases for all real (irreversible) ones. A system that is not isolated can lose entropy if energy leaves it.

Key ideas

• Temperature measures average particle kinetic energy.
• PV = nRT relates pressure, volume and temperature.
• ΔU = Q + W (W = work done on the gas).
• Work on a PV diagram equals the area under the curve.
• No heat engine can exceed the Carnot efficiency.

Formulas and rules

Common mistakes

• Using Celsius instead of kelvins in gas laws and efficiency.
• Mixing sign conventions: AP uses W as work done on the gas.

Words to know

Temperature

A measure of the average kinetic energy of particles.

Ideal gas law

PV = nRT.

Kinetic theory

Explains gas behavior through particle motion.

Thermal equilibrium

No net heat flow between objects at the same temperature.

Heat

Energy transferred because of a temperature difference.

Conduction

Heat transfer through direct contact.

Convection

Heat transfer by fluid movement.

Radiation

Heat transfer by electromagnetic waves.

Internal energy

The total kinetic and potential energy of a system's particles.

First law of thermodynamics

ΔU = Q + W.

Isobaric process

A process at constant pressure.

Isochoric process

A process at constant volume.

Isothermal process

A process at constant temperature.

Adiabatic process

A process with no heat transfer.

PV diagram

A graph of pressure versus volume.

Entropy

A measure of disorder or energy dispersal.

Second law of thermodynamics

Entropy of an isolated system never decreases.

Heat engine

A device that converts heat into work.

Carnot efficiency

The maximum efficiency of a heat engine.

Sample practice questions

13 more questions like these, from level 1 to 5, are in the practice set.