AP Physics 2: Thermodynamics

Thermodynamics in AP Physics 2 connects microscopic particle behavior to macroscopic quantities you can measure: temperature, pressure, volume, internal energy, and entropy. It is the physics of why hot objects cool, why gases expand when heated, and why no engine can convert heat into work with 100% efficiency. Mastering this unit means learning a small set of core ideas and applying them consistently across different situations.

Heat, Temperature, and Thermal Equilibrium

A common early challenge is separating temperature from heat.

• Temperature measures how “hot” something is and is tied to the average kinetic energy of particles. It is an intensive property, meaning it does not depend on the amount of substance.
• Heat is energy transferred because of a temperature difference. Heat is not something an object “contains”; it is a process, measured in joules.

When two systems are placed in contact, energy transfers from the higher temperature system to the lower temperature system until they reach thermal equilibrium, meaning their temperatures become equal. The zeroth law of thermodynamics formalizes this: if A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. This matters because it justifies the use of thermometers as reliable comparators.

Kinetic Theory: Microscopic Picture of a Gas

In kinetic theory, an ideal gas is modeled as many particles in constant random motion, colliding elastically with each other and the container walls. Pressure arises from those collisions. Temperature corresponds to the average translational kinetic energy of the gas particles.

For a monatomic ideal gas, the internal energy depends only on temperature:

• $U\propto T$

On the AP level, you typically use the idea that increasing temperature increases internal energy, and for an ideal gas, internal energy does not depend directly on volume or pressure, only on temperature.

Heat Transfer: Conduction, Convection, Radiation

Heat moves in three main ways, and problems often ask you to identify which mechanism dominates.

Conduction

Conduction transfers energy through direct contact and microscopic collisions within a material. Metals conduct well because free electrons carry energy efficiently, while wood and air are poor conductors.

In steady-state conduction across a slab, the rate depends on temperature difference, area, thickness, and thermal conductivity. Conceptually: larger area and larger temperature difference increase heat flow; thicker materials reduce it.

Convection

Convection is heat transfer by bulk fluid motion. Warm fluid becomes less dense and rises while cooler fluid sinks, forming circulation. It is common in boiling water, atmospheric patterns, and home heating.

Radiation

Radiation transfers energy via electromagnetic waves and does not require a medium. Any object above absolute zero emits radiation. Dark, matte surfaces absorb and emit more effectively than shiny reflective ones, which is why reflective insulation and thermal blankets can reduce radiative losses.

The Ideal Gas Law and What It Really Says

The ideal gas law links macroscopic variables:

• $PV=nRT$

Here, $P$ is pressure, $V$ volume, $n$ moles, $R$ the gas constant, and $T$ absolute temperature (kelvin). It is a model that works well for many gases at low pressure and moderate temperature. It can fail when gases are dense or near condensation, when intermolecular forces and particle volume matter.

A practical AP skill is recognizing proportional relationships. For fixed $n$:

• At constant $V$, $P\propto T$
• At constant $P$, $V\propto T$
• At constant $T$, $PV=\text{constant}$

The First Law of Thermodynamics: Energy Accounting

The first law is the thermodynamics version of conservation of energy:

• $\Delta U=Q-W$

$\Delta U$ is the change in internal energy, $Q$ is heat added to the system, and $W$ is work done by the system. Sign conventions are crucial. If the system expands and pushes the surroundings, $W$ is positive. If heat flows into the system, $Q$ is positive.

Work and PV Diagrams

For many AP problems, work is found from a PV diagram. When a gas changes volume, the work done by the gas is the area under the curve: $$W=\int PdV$$

• Expansion (moving right) typically gives positive work.
• Compression (moving left) gives negative work.

PV diagrams are also a powerful way to interpret processes:

Isothermal (constant temperature)

For an ideal gas, isothermal processes satisfy $PV=\text{constant}$. Internal energy stays constant because $U$ depends only on $T$, so:

• $\Delta U=0$, therefore $Q=W$

Isochoric (constant volume)

No volume change means no boundary work:

• $W=0$, so $\Delta U=Q$

Isobaric (constant pressure)

Work is straightforward:

• $W=P\Delta V$

Adiabatic (no heat transfer)

If $Q=0$, then:

• $\Delta U=-W$

Adiabatic expansion cools a gas because it does work while receiving no heat. This is a real-world idea behind cooling in expanding air masses and some refrigeration stages.

The Second Law, Entropy, and Irreversibility

The second law of thermodynamics explains why some processes happen spontaneously and others do not. Heat can flow from hot to cold on its own, but not from cold to hot without external work.

This is where entropy enters. Entropy is a measure tied to the number of microscopic arrangements consistent with a macrostate, often summarized as “disorder,” though that can be misleading. A more reliable AP interpretation is:

• In an isolated system, total entropy tends to increase or stay the same.

For reversible heat transfer at temperature $T$, the entropy change is:

• $\Delta S=\frac{Q_{\text{rev}}}{T}$

Even if you are not calculating entropy often, you must reason with it. Mixing two fluids at different temperatures increases total entropy. Friction converts organized mechanical energy into thermal energy spread among many microstates, increasing entropy. These processes are effectively irreversible.

Heat Engines, Efficiency, and the Carnot Limit

A heat engine converts heat input into net work by operating in a cycle. It takes in heat $Q_H$ from a hot reservoir, expels heat $Q_C$ to a cold reservoir, and produces work:

• $W_{\text{net}}=Q_H-Q_C$

Efficiency measures how much input heat becomes useful work:

• $e=\frac{W_{\text{net}}}{Q_H}=1-\frac{Q_C}{Q_H}$

No engine can have $e=1$ because the second law requires some heat to be rejected to a colder reservoir.

Carnot Engine and Maximum Efficiency

The Carnot engine is an ideal reversible engine that sets the maximum possible efficiency between two reservoirs:

• $e_{\text{Carnot}}=1-\frac{T_C}{T_H}$

Temperatures must be in kelvin. This equation is not about engineering details; it is a deep statement that efficiency is limited by the temperature difference, not by clever mechanics. To improve efficiency, you either raise $T_H$ (hotter source) or lower $T_C$ (colder sink), but both are constrained by material limits and environmental conditions.

Refrigerators and Heat Pumps (Reverse Engines)

A refrigerator uses work to move heat from cold to hot. Instead of efficiency, the key metric is the coefficient of performance (COP). Conceptually, the main point is that moving heat “uphill” in temperature requires energy input, consistent with the second law.

How to Think Like an AP Physics Student in Thermodynamics

Thermodynamics problems become manageable when you adopt a consistent toolkit:

1. Define the system (gas in a piston, air in a room, water in a cup).
2. Track signs for $Q$ and $W$ using $\Delta U=Q-W$.
3. Use PV diagrams to interpret work as area under the curve.
4. Use ideal gas reasoning only when appropriate and always use kelvin.
5. Apply the second law qualitatively: if a claim implies 100% conversion of heat to work in a cycle, or spontaneous heat flow from cold to hot, it is wrong.

AP Physics 2 thermodynamics is less about memorizing equations and more about disciplined reasoning: energy is conserved, entropy sets direction, and cycles have unavoidable limits. If you can connect those three ideas to PV graphs and the ideal gas model, you have the unit’s core.