热力学

• 9.1.A.1 Atoms in a gas collide with and exert forces on other atoms in the gas and with the container in which the gas is contained.
  • 9.1.A.1.i Collisions involving pairs of atoms or an atom and a fixed object can be described and analyzed using conservation of momentum principles.
  • 9.1.A.1.ii The pressure exerted by a gas on a surface is the ratio of the sum of the magnitudes of the perpendicular components of the forces exerted by the gas's atoms on the surface to the area of the surface.
    • Equation: $P = \dfrac{F_{\perp}}{A}$
  • 9.1.A.1.iii Pressure exists throughout the gas itself, not just at the boundary between the gas and the container.

• 9.1.B.1 The temperature of a system is characterized by the average kinetic energy of the atoms within that system.
  • 9.1.B.1.i The Maxwell–Boltzmann distribution provides a graphical representation of the energies and speeds of atoms at a given temperature.
  • 9.1.B.1.ii The root-mean-square speed corresponding to the average kinetic energy for an ideal gas is related to the temperature of the gas by
    • Equation: $K_{\text{avg}} = \dfrac{3}{2} k_B T = \dfrac{1}{2} m v_{\text{rms}}^2$

Boundary statement: AP Physics 2 only expects students to perform qualitative and quantitative analysis of collisions in one and two dimensions. Students are not expected to know the functional form of the Maxwell-Boltzmann distribution but are expected to be familiar with how features of the distribution are related to the temperature of the gas.

• 9.2.A.1 The classical model of an ideal gas assumes that the instantaneous velocities of atoms are random, the volumes of the atoms are negligible compared to the total volume occupied by the gas, the atoms collide elastically, and the only appreciable forces on the atoms are those that occur during collisions.
• 9.2.A.2 An ideal gas is one in which the relationships between pressure, volume, the number of moles or number of atoms, and temperature of a gas can be modeled using the equation
  • Equation: $PV = nRT = N k_B T$
• 9.2.A.3 Graphs modeling the pressure, temperature, and volume of gases can be used to describe or determine properties of that gas.
• 9.2.A.4 A temperature at which an ideal gas has zero pressure can be extrapolated from a graph of pressure as a function of temperature.

• 9.3.A.1 Two systems are in thermal contact if the systems may transfer energy by thermal processes.
  • 9.3.A.1.i Heating is the transfer of energy into a system by thermal processes.
  • 9.3.A.1.ii Cooling is the transfer of energy out of a system by thermal processes.
• 9.3.A.2 The thermal processes by which energy may be transferred between systems at different temperatures are conduction, convection, and radiation.
• 9.3.A.3 Energy is transferred through thermal processes spontaneously from a higher-temperature system to a lower-temperature system.
  • 9.3.A.3.i In collisions between atoms from different systems, energy is most likely to be transferred from higher-energy atoms to lower-energy atoms.
  • 9.3.A.3.ii After many collisions of atoms from different systems, the most probable state is one in which both systems have the same temperature.
• 9.3.A.4 Thermal equilibrium results when no net energy is transferred by thermal processes between two systems in thermal contact with each other.

• 9.4.A.1 The internal energy of a system is the sum of the kinetic energy of the objects that make up the system and the potential energy of the configuration of those objects.
  • 9.4.A.1.i The atoms in an ideal gas do not interact with each other via conservative forces, and the internal structure is not considered. Therefore, an ideal gas does not have internal potential energy.
  • 9.4.A.1.ii The internal energy of an ideal monatomic gas is the sum of the kinetic energies of the constituent atoms in the gas.
    • Equation: $U = \dfrac{3}{2} nRT = \dfrac{3}{2} N k_B T$
• 9.4.A.2 Changes to a system's internal energy can result in changes to the internal structure and internal behavior of that system without changing the motion of the system's center of mass.

• 9.4.B.1 The first law of thermodynamics is a restatement of conservation of energy that accounts for energy transferred into or out of a system by work, heating, or cooling.
  • 9.4.B.1.i For an isolated system, the total energy is constant.
  • 9.4.B.1.ii For a closed system, the change in internal energy is the sum of energy transferred to or from the system by heating, or work done on the system.
    • Equation: $\Delta U = Q + W$
  • 9.4.B.1.iii The work done on a system by a constant or average external pressure that changes the volume of that system (for example, a piston compressing a gas in a container) is defined as
    • Equation: $W = -P \Delta V$
• 9.4.B.2 Pressure-volume graphs (also known as PV diagrams) are representations used to represent thermodynamic processes.
  • 9.4.B.2.i Lines of constant temperature on a PV diagram are called isotherms.
  • 9.4.B.2.ii The absolute value of the work done on a gas when the gas expands or compresses is equal to the area underneath the curve of a plot of pressure vs. volume for the gas.
• 9.4.B.3 Special cases of thermal processes depend on the relationship between the configuration of the system, the nature of the work done on the system, and the system's surroundings. These include constant volume (isovolumetric), constant temperature (isothermal), and constant pressure (isobaric), as well as processes where no energy is transferred to or from the system through thermal processes (adiabatic).

• 9.5.A.1 The amount of energy required to change the temperature of a material is related to the material's specific heat.
  • Equation: $Q = mc\Delta T$
• 9.5.A.2 The specific heat of a material is an intrinsic property of that material that depends on the arrangement and interactions of the atoms that make up the material.

• 9.5.B.1 The rate at which energy is transferred by conduction through a given material is related to the thermal conductivity, the physical dimensions of the material, and the temperature difference across the material.
  • Equation: $\dfrac{Q}{\Delta t} = \dfrac{kA\Delta T}{L}$
• 9.5.B.2 The thermal conductivity of a material is an intrinsic property of that material that depends on the arrangement and interactions of the atoms that make up the material.

Boundary statement: AP Physics 2 will model specific heat as independent of temperature.

• 9.6.A.1 The second law of thermodynamics states that the total entropy of an isolated system can never decrease and is constant only when all processes the system undergoes are reversible.
• 9.6.A.2 Entropy can be qualitatively described as the tendency of energy to spread or the unavailability of some of the system's energy to do work.
  • 9.6.A.2.i Localized energy will tend to disperse and spread out.
  • 9.6.A.2.ii Entropy is a state function and therefore only depends on the current state or configuration of a system, not how the system reached that state.
  • 9.6.A.2.iii Maximum entropy occurs when a system is in thermodynamic equilibrium.
• 9.6.A.3 The change in a system's entropy is determined by the system's interactions with its surroundings.
  • 9.6.A.3.i Isolated systems spontaneously move toward thermodynamic equilibrium.
  • 9.6.A.3.ii The entropy of an isolated system never decreases, but the entropy of a closed system can decrease because energy can be transferred into or out of the system.

Boundary statement: Only qualitative treatment of the second law of thermodynamics is within the scope of AP Physics 2.