Heat and Energy Transfer — AP Physics 2
1. Core Definitions: Heat, Temperature, and Equilibrium ★★☆☆☆ ⏱ 3 min
Heat is defined as the transfer of thermal energy between two systems that occurs exclusively due to a temperature difference between the systems. In AP Physics 2 notation, heat is denoted $Q$, with the sign convention that $Q>0$ means heat is added to the system of interest, and $Q<0$ means heat leaves the system. A key distinction: heat is energy in transit, not energy stored in a system. Stored thermal energy is called internal energy; temperature is the macroscopic driving force for heat transfer. Net heat transfer stops when systems reach thermal equilibrium, meaning they have the same temperature. This topic makes up ~30% of Unit 2, or 7-9% of your total exam score, and appears in both MCQ and FRQ sections.
2. Heat Capacity and Calorimetry ★★★☆☆ ⏱ 5 min
The relationship between heat transferred to a substance and its resulting temperature change is governed by specific heat capacity $c$, defined as the amount of energy required to raise the temperature of 1 kilogram of the substance by 1 Kelvin (or 1 degree Celsius, since temperature changes are identical in both scales). The fundamental formula is:
Q = mc\Delta T
where $m$ is mass of the substance, and $\Delta T = T_{final} - T_{initial}$ is the temperature change. For an insulated system (no heat exchanged with the surroundings), total energy is conserved, so total heat gained by colder substances equals total heat lost by warmer substances: $Q_{gained} = Q_{lost}$. This relationship is the basis of calorimetry, the experimental method for measuring specific heat capacity.
Exam tip: If your final equilibrium temperature is outside the range of the two initial temperatures, you mixed up the direction of heat transfer. Rewrite the equation so both sides are positive to fix the error.
3. Conduction and Convection ★★★☆☆ ⏱ 4 min
There are three distinct modes of heat transfer, two of which require a material medium: conduction and convection. Conduction is heat transfer via molecular collisions through a stationary material (no bulk motion of the material itself). For steady-state conduction through a uniform slab of material, Fourier's Law gives the rate of heat transfer (power, $P = Q/\Delta t$):
P = \frac{kA\Delta T}{L}
where $k$ is thermal conductivity (high for metals, low for insulators like air or wool), $A$ is the cross-sectional area of the slab, $L$ is the thickness of the slab, and $\Delta T$ is the temperature difference across the slab. Convection is heat transfer via bulk motion of a fluid (liquid or gas). Natural convection occurs when warm fluid is less dense than cool fluid, causing it to rise and carry heat away from a warm surface; forced convection occurs when an external force (like a fan or pump) moves fluid across the surface, increasing heat transfer rate. AP Physics 2 does not require a detailed formula for convection, only identification of when it is the dominant mode.
Exam tip: Always check the units of $k$ before plugging in length values. Most $k$ values use meters, so convert millimeters or centimeters to meters to avoid orders-of-magnitude errors.
4. Thermal Radiation and Stefan-Boltzmann Law ★★★★☆ ⏱ 4 min
All objects with a temperature above absolute zero emit thermal radiation, which is electromagnetic radiation that can travel through a vacuum (no material medium required). The total power emitted by an object is given by the Stefan-Boltzmann Law:
P = \sigma A e T^4
where $\sigma = 5.67 \times 10^{-8} W m^{-2} K^{-4}$ is the Stefan-Boltzmann constant, $A$ is the surface area of the object, $e$ is emissivity (a value between 0 for a perfect reflector and 1 for a perfect blackbody radiator), and $T$ is the absolute temperature of the object in Kelvin. An object also absorbs radiation from its surroundings, so the net rate of heat transfer via radiation is:
P_{net} = \sigma A e (T^4 - T_s^4)
where $T_s$ is the absolute temperature of the surroundings. If $T > T_s$, the object has a net heat loss; if $T < T_s$, it has a net gain. The $T^4$ dependence means radiation increases very rapidly with temperature.
Exam tip: You must convert temperature to Kelvin for the Stefan-Boltzmann Law. Using Celsius will give a completely wrong result, because the law depends on absolute temperature, not temperature relative to freezing.
Common Pitfalls
Why: Students are accustomed to using Celsius for $\Delta T$ in $Q=mc\Delta T$, so they forget the $T^4$ term requires absolute temperature
Why: Everyday language uses 'heat' interchangeably with 'hotness', which conflicts with the strict physics definition
Why: Students blindly plug $\Delta T = T_f - T_i$ into $Q=mc\Delta T$ for all substances, leading to incorrect sign cancellation
Why: Students confuse the requirements for conduction/convection with radiation
Why: Thicknesses are often quoted in smaller units for convenience, and students forget unit conversion to match thermal conductivity units