---
title: "Fourier's Law of Heat Conduction — AP Physics 2 Guide"
description: "Fourier's law, Q/Δt = kAΔT/L, gives the rate of heat conduction through a material. Learn how AP Physics 2 tests it in Unit 9 and how it mirrors Ohm's law."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/fouriers-law-of-heat-conduction"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 9"
---

# Fourier's Law of Heat Conduction — AP Physics 2 Guide

## Definition

Fourier's law of heat conduction says the rate of thermal energy transfer through a material is Q/Δt = kAΔT/L, so heat flows faster with higher thermal conductivity (k), bigger cross-sectional area (A), and larger temperature difference (ΔT), but slower through thicker material (L). Tested in AP Physics 2 Topic 9.5.

## What It Is

Fourier's law of heat conduction is the equation that tells you **how fast** thermal energy moves through a material by conduction. In [AP Physics 2](/ap-physics-2-revised "fv-autolink") form, it's written as Q/Δt = kAΔT/L. The left side is a rate, energy per time, measured in watts. The right side breaks down into four physical ingredients. [Thermal conductivity](/ap-physics-2-revised/key-terms/thermal-conductivity "fv-autolink") k is an intrinsic property of the material that depends on how its atoms are arranged and how they interact (metals conduct well, styrofoam doesn't). A is the cross-sectional area the heat flows through, ΔT is the temperature difference driving the flow, and L is the thickness the heat has to cross.

The intuition is simple. Heat conduction is a traffic flow problem. A bigger temperature difference pushes harder, a wider area gives more lanes, a better conductor is a smoother road, and a thicker wall is a longer trip. Notice it's the only [thermodynamics](/ap-physics-2-revised/unit-9 "fv-autolink") equation in the course with time in it. Q = mcΔT tells you how much energy a temperature change requires; Fourier's law tells you how quickly that energy actually gets there.

## Why It Matters

This equation lives in **Unit 9: Thermodynamics, [Topic 9.5](/ap-physics-2-revised/unit-9/5-specific-heat-and-thermal-conductivity/study-guide/VTemzlLtvNgPkUnm "fv-autolink") (Specific Heat and Thermal Conductivity)** and directly supports learning objective **9.5.B**, which asks you to describe the rate at which energy is transferred by conduction through a given material. The CED's essential knowledge spells out exactly what the exam cares about. The rate depends on thermal conductivity, the physical dimensions of the material, and the [temperature difference](/ap-physics-2-revised/key-terms/temperature-difference "fv-autolink") across it, and thermal conductivity is an intrinsic property tied to atomic structure. That last point matters because the exam loves intrinsic vs. extensive property reasoning. Changing the shape of a block changes A and L, but it can never change k. Fourier's law is also your quantitative backup for a core thermodynamics idea: heat spontaneously flows from hot to cold, and this equation tells you how fast.

## Connections

### Q = mcΔT, Specific Heat (Unit 9)

These two equations share Topic 9.5 and answer different questions about the same heat. Q = mcΔT tells you the total [energy](/ap-physics-2-revised/unit-15/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf "fv-autolink") needed to change a temperature, while Fourier's law tells you the rate that energy conducts through a material. A classic two-step problem uses Fourier's law to find how fast heat enters an object, then Q = mcΔT to find how its temperature changes.

### Direction of Heat Flow and Entropy (Unit 9)

Thermodynamics says heat spontaneously flows from hot to cold, and Fourier's law puts a number on it. ΔT is the driving force, and when ΔT hits zero the objects are at [thermal equilibrium](/ap-physics-2-revised/key-terms/thermal-equilibrium "fv-autolink") and conduction stops. The equation is the second law's hot-to-cold rule turned into a calculable rate.

### Ohm's Law and Resistance (Unit 11)

Fourier's law is structurally Ohm's law for heat. Temperature difference plays the role of [voltage](/ap-physics-2-revised/key-terms/voltage "fv-autolink"), heat flow rate plays the role of current, and L/(kA) acts like resistance. Compare it to R = ρL/A for a resistor, where longer and skinnier means more resistance. If you can reason about circuits, you can reason about conduction, and vice versa.

## On the AP Exam

Fourier's law shows up almost entirely as **proportional reasoning**. Expect multiple-choice stems like "if the slab's thickness doubles and its area doubles, what happens to the rate of heat transfer?" (it stays the same, since A and L cancel) or ranking tasks comparing rods of different materials, lengths, and areas. You should be able to identify that k is intrinsic to the material while A and L are geometric, explain why the rate drops as the system approaches thermal equilibrium (ΔT shrinks), and recognize that Q/Δt has units of watts because it's power. No released FRQ has used the name "Fourier's law" verbatim, but conduction-rate reasoning is fair game in any Unit 9 question, especially paired with Q = mcΔT in multi-step energy problems. The equation appears on the AP Physics 2 equation sheet, so the test is whether you can interpret it, not memorize it.

## Fourier's Law of Heat Conduction vs Q = mcΔT (specific heat equation)

Both live in Topic 9.5 and both contain Q and ΔT, but they answer different questions. Q = mcΔT gives a total amount of energy for a temperature change within one object, with no time involved. Fourier's law gives a rate of energy transfer between two regions at different temperatures, and time is the whole point. Also watch the ΔT trap. In Q = mcΔT, ΔT is the change in one object's temperature over time. In Fourier's law, ΔT is the difference between the two sides of the material at one moment.

## Key Takeaways

- Fourier's law, Q/Δt = kAΔT/L, gives the rate of heat conduction in watts, not a total amount of energy.
- Heat conducts faster with higher thermal conductivity, larger cross-sectional area, and bigger temperature difference, and slower through thicker material.
- Thermal conductivity k is an intrinsic property determined by the arrangement and interactions of a material's atoms, so reshaping an object changes A and L but never k.
- As two objects approach thermal equilibrium, ΔT shrinks toward zero, so the conduction rate slows down and eventually stops.
- Fourier's law works like Ohm's law for heat, with ΔT acting like voltage, Q/Δt acting like current, and L/(kA) acting like resistance.
- Use Fourier's law to find how fast energy flows, then Q = mcΔT to find how much an object's temperature changes as a result.

## FAQs

### What is Fourier's law of heat conduction in AP Physics 2?

It's the equation Q/Δt = kAΔT/L, which gives the rate of thermal energy transfer by conduction through a material. The rate increases with thermal conductivity k, area A, and temperature difference ΔT, and decreases with thickness L. It's part of Topic 9.5 in Unit 9 (Thermodynamics).

### Is Fourier's law on the AP Physics 2 equation sheet?

Yes. The equation Q/Δt = kAΔT/L is given on the equation sheet, so the exam tests interpretation and proportional reasoning, not memorization. You need to know what each variable means and how changing one affects the rate.

### Does a thicker wall conduct heat faster because it has more material?

No, the opposite. Thickness L sits in the denominator, so doubling the thickness cuts the conduction rate in half. More material between hot and cold means a longer path for the energy, which is exactly why thick insulation works.

### How is thermal conductivity different from specific heat?

Thermal conductivity (k) measures how fast heat moves through a material; specific heat (c) measures how much energy it takes to raise the material's temperature. Both are intrinsic properties, but k belongs to Fourier's law (a rate) and c belongs to Q = mcΔT (a total energy).

### Does Fourier's law cover convection and radiation too?

No. Fourier's law describes conduction only, where energy passes through a material via atomic interactions. The AP Physics 2 CED keeps the quantitative rate equation to conduction, which is why ΔT is measured across a solid slab or rod of thickness L.

## Related Study Guides

- [9.5 Specific Heat and Thermal Conductivity](/ap-physics-2-revised/unit-9/5-specific-heat-and-thermal-conductivity/study-guide/VTemzlLtvNgPkUnm)

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