Conduction vs Convection: The Difference

The distinction, stated once

Both are ways energy crosses from a hotter place to a cooler one, and essential knowledge 9.3.A.2 lists them together: the thermal processes by which energy may be transferred between systems at different temperatures are conduction, convection, and radiation. Three processes, one list, and the difference between the first two is whether the matter travels.

Conduction passes energy along without moving the material. Particles at the hot end are moving faster, they collide with their neighbors, the neighbors speed up and collide with theirs, and the disturbance propagates. The metal spoon in a hot drink is in the same place after the handle warms as it was before. Because nothing has to flow, conduction is the process that works in solids.

Convection moves the material and lets it carry its energy along. Warm fluid moves bodily from one region to another and arrives with the internal energy it already had. Nothing is passed from particle to particle; the particles themselves relocate. Because the matter has to travel, convection needs a fluid and cannot happen in a solid.

So the test is a question about the material, not about the energy: did the stuff move, or only the energy?

That is the physics. Before going further it is worth being straight about the exam, because the two processes are not treated equally by the course at all, and the next section is about that.

Check the scope first: one of these has an equation and the other does not

AP Physics 2 gives conduction its own learning objective and a printed rate equation. It gives convection a single mention.

Conduction is quantitative. Learning objective 9.5.B, in Topic 9.5, Specific Heat and Thermal Conductivity, is to describe the rate at which energy is transferred by conduction through a given material. Essential knowledge 9.5.B.1 says that rate is related to the thermal conductivity, the physical dimensions of the material, and the temperature difference across the material, with the relevant equation

That equation is printed on the AP Physics 2 equation sheet, in the Thermal Physics panel, and the panel's symbol list defines $k$ as thermal conductivity, $A$ as area and $L$ as length. Essential knowledge 9.5.B.2 adds that 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.

Convection is not quantitative, and it is not really qualitative either. The word convection appears in the AP Physics 2 CED exactly twice. Once in 9.3.A.2, as one of the three named thermal processes. Once in the appendix's vocabulary section on heat, again inside a list of thermal processes. That is the whole of it. There is no learning objective about convection, no essential knowledge statement of its own, no equation, no constant in the constants box, and no boundary statement limiting how it is treated, because there is nothing to limit. Do not learn a convection formula for this exam. Whatever coefficient of convective heat transfer you may have met elsewhere, the AP course does not use it and could not ask you to.

Neither word appears anywhere in the AP Physics 1 CED. Thermal energy transfer is an AP Physics 2 topic in this course sequence.

Radiation, the third item on the list, sits in between and it is worth knowing where. In Unit 9 it is named alongside the other two in 9.3.A.2 and left there. It becomes quantitative in a different unit: 15.4.A.3.iii, in Unit 15, Modern Physics, says the rate at which energy is emitted by a blackbody is proportional to the surface area of the body and to the temperature of the body raised to the fourth power, as described by the Stefan-Boltzmann law, with the relevant equation $P = A\sigma T^4$. That equation is printed in the Modern Physics panel of the sheet, and the constants box supplies $\sigma = 5.67 \times 10^{-8}\ \text{W/(m}^2 \cdot \text{K}^4)$.

So of the three processes named in one sentence of 9.3.A.2, two acquire equations in different units of the course and one never does.

Conduction against convection, row by row

Rows six through nine are the practical content of this page, and row seven is the one that decides how to revise. There is a number to compute on one side and nothing to compute on the other.

Row eleven is where the two are genuinely alike, and it is worth saying because it is the part that is examinable for both. 9.3.A.3 states that energy is transferred through thermal processes spontaneously from a higher-temperature system to a lower-temperature system, and the statement covers all three processes without distinguishing them. It is supported by 9.3.A.3.i, which says that in collisions between atoms from different systems, energy is most likely to be transferred from higher-energy atoms to lower-energy atoms, and 9.3.A.3.ii, which says that 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 then defines the endpoint: thermal equilibrium results when no net energy is transferred by thermal processes between two systems in thermal contact with each other.

So the direction and the destination are shared. Only the mechanism, and the exam treatment, differ.

The conduction rate equation, factor by factor

Since this is the half of the pair you can be asked to compute, it is worth reading the equation slowly. 9.5.B.1 gives

Four things on the right, and each one behaves differently.

• $k$, the thermal conductivity. 9.5.B.2 calls it an intrinsic property of the material, depending on the arrangement and interactions of its atoms. Intrinsic means it belongs to the substance, not to the slab: cutting a copper bar in half does not change $k$. Its unit follows from the equation, watts per meter per kelvin. No values of $k$ are printed on the equation sheet, so a question that needs one has to supply it.
• $A$, the area across which the energy flows, perpendicular to the flow. Doubling the area doubles the rate, which is why a large window loses more than a small one made of the same glass.
• $\Delta T$, the temperature difference across the material, not the temperature of either side. A difference in kelvin and a difference in degrees Celsius are the same number, so this is one of the few places you do not need to convert. Celsius vs Kelvin sets out when you do.
• $L$, the thickness the energy has to cross. It is in the denominator, so a thicker layer conducts more slowly. Doubling the thickness halves the rate.

Notice what the left side is. $Q/\Delta t$ is a rate, energy per unit time, measured in watts. It is not an amount of energy, and a question asking how much energy crosses in a given interval wants you to multiply by that interval. This is the commonest arithmetic slip on the topic.

Notice also what is missing. There is no time dependence, no mass, and no specific heat. The equation gives the steady rate at which energy crosses a slab, and it says nothing about what happens to the energy once it arrives. That is the other half of Topic 9.5: 9.5.A.1 gives $Q = mc\Delta T$ for the energy required to change a material's temperature, and 9.5.A.2 says the specific heat of a material is an intrinsic property that depends on the arrangement and interactions of the atoms making it up, in wording deliberately parallel to 9.5.B.2. Two intrinsic properties, one governing how fast energy moves through and the other how much energy a temperature change costs.

The case that separates them: why the tile floor feels colder than the mat

This is Unit 9's own opening question. The CED prints it as one of the unit's essential questions: why does the tile floor in the bathroom feel so much colder than the bathroom mat?

The two are at the same temperature. They have both been sitting in the same room all night. A thermometer laid on each reads the same number. So whatever your foot is detecting, it is not temperature.

What your foot detects is the rate at which energy leaves it, and that is a conduction question with $k$ as the only thing that differs.

Take a contact patch of $0.010\ \text{m}^2$, a surface layer $0.005\ \text{m}$ thick, and skin at $33\ \text{C}$ against a room at $20\ \text{C}$, so $\Delta T = 13\ \text{K}$. Suppose a question supplies $k = 1.1\ \text{W/(m} \cdot \text{K)}$ for the tile and $k = 0.050\ \text{W/(m} \cdot \text{K)}$ for the mat.

A factor of $22$. Over ten seconds the tile draws $286\ \text{J}$ out of your foot and the mat draws $13\ \text{J}$. Same temperature, same area, same thickness, same temperature difference, and one of them is pulling energy out twenty-two times faster.

This is the cleanest demonstration on the page of what conduction is, and it makes two points at once.

First, conduction is a rate, not a state. Cold is not a substance the tile has more of. The tile is not colder, it conducts faster, and your nerve endings report a rate of energy loss rather than a temperature. Heat vs temperature is the page for that confusion in general.

Second, convection is not in this story at all. Nothing about the tile or the mat is flowing anywhere. Both are solids, and a solid cannot convect. If the same question were asked about standing in a draft rather than on a floor, convection would be the answer and there would be no equation to reach for. That asymmetry is the exam-relevant one: the situations the course can make you compute are conduction situations, by construction.

What an exam can actually ask about convection

Not a calculation. With no equation and no material constant in the course, no question can require a convective number. What is left is identification and reasoning, and both are supported by the skill list attached to Topic 9.3: 1.A, create diagrams, tables, charts, or schematics to represent physical situations; 2.C, compare physical quantities between two or more scenarios; 3.B, apply an appropriate law, definition, theoretical relationship, or model to make a claim; and 3.C, justify or support a claim using evidence.

So the reasonable expectations are these.

• Name the process operating in a described situation, given that 9.3.A.2 supplies the list of three.
• State the direction of the transfer, which 9.3.A.3 fixes as spontaneously from higher temperature to lower temperature, whichever of the three processes is at work.
• Say when the transfer stops, which 9.3.A.4 defines as thermal equilibrium, when no net energy is transferred between two systems in thermal contact.
• Recognize that all three deliver energy to the same first law. Whichever mechanism carried it, the energy arrives as $Q$ in $\Delta U = Q + W$, and the mechanism leaves no trace in the result.

The distinguishing feature to have ready, if you are asked to justify a choice, is the one from the first section: convection requires the material itself to move in bulk, conduction does not. A sealed solid wall cannot convect. A pot of water on a stove does both at once, conducting through the metal base and convecting within the water.

What you should not write is a convective analogue of $Q/\Delta t = kA\Delta T/L$. The AP Physics 2 course does not define one, and inventing a coefficient in a free-response answer spends time on something no rubric can credit.

When it costs a mark

• Reporting a rate as an energy. $Q/\Delta t$ is in watts. A question asking how much energy crossed a wall in an hour needs the rate multiplied by $3600\ \text{s}$, and $5400\ \text{W}$ becomes $1.944 \times 10^7\ \text{J}$.
• Putting $L$ in the numerator. Thickness is in the denominator: thicker insulates better. Checking the direction of one factor before substituting catches this instantly.
• Using one side's temperature instead of the difference. The equation contains $\Delta T$ across the material. A wall between $21\ \text{C}$ and $3\ \text{C}$ has $\Delta T = 18\ \text{K}$, not $294\ \text{K}$.
• Converting a temperature difference to kelvin. A difference is already the same in both scales, so $18\ \text{C}$ of difference is $18\ \text{K}$ of difference. Adding $273$ to a difference is a real and costly error.
• Treating $k$ as a property of the slab. 9.5.B.2 calls thermal conductivity an intrinsic property of the material. The slab's area and thickness are separate factors in the equation, and confusing the two turns a material comparison into a geometry comparison.
• Confusing thermal conductivity with specific heat. Both are intrinsic, both are described in parallel wording by 9.5.B.2 and 9.5.A.2, and both live in Topic 9.5. $k$ sets how fast energy crosses a material, $c$ sets how much energy a temperature change costs, and they appear in different equations.
• Answering a convection question with a formula. There is none in this course, and writing one signals that the scope was not checked.
• Calling any transfer through a fluid convection. A fluid conducts too. Convection specifically requires the fluid to move in bulk and carry energy with it, so a still layer of trapped air between two panes is conducting, not convecting.

When they run together, and why that lulls you

In almost every real situation both processes are working at once, which is why they are hard to keep separate in the first place.

A saucepan on a stove conducts through the metal base and then convects inside the water. A house loses energy by conducting through the walls and by convecting through the draughts. A cup of coffee conducts into the ceramic, convects within the liquid, and radiates from the surface, all simultaneously and all in the same direction, from hot to cold. Nothing in the outcome labels which fraction went by which route.

And that is the deeper reason the distinction is easy to lose: the first law does not care. All three processes deliver their energy as $Q$, the same $Q$ that appears in $\Delta U = Q + W$, and the equation sheet's symbol list defines $Q$ simply as the energy transferred to a system by heating, with no subdivision by mechanism. Once the energy has arrived, the route it took has left no trace in the internal energy or the temperature.

So the three mechanisms matter for exactly one thing: predicting how fast, or in the case of an insulated container, whether at all. They never matter for the bookkeeping afterwards.

One more overlap worth naming, because it is the standard exam trap. Insulation usually works by trapping a fluid so it cannot convect. Double glazing, foam, a duvet, and the fur on an animal all rely on a layer of still air, and still air conducts poorly. The situation looks like it is about convection, since preventing convection is the design goal, but the physics that survives is conduction, and conduction is the half with the equation. If a question about an insulating layer expects a number, the number comes from $Q/\Delta t = kA\Delta T/L$ applied to whatever is left after the bulk motion has been stopped.

What the CED asks of Topics 9.3 and 9.5

Both processes belong to AP Physics 2 Unit 9, Thermodynamics, weighted at $15$ to $18\ \%$ of the multiple-choice section across a suggested $10$ to $16$ class periods.

Topic 9.3, Thermal Energy Transfer and Equilibrium, has one learning objective, 9.3.A, to describe the transfer of energy between two systems in thermal contact due to temperature differences of those two systems. Its essential knowledge is:

• 9.3.A.1, two systems are in thermal contact if the systems may transfer energy by thermal processes, with 9.3.A.1.i defining heating as the transfer of energy into a system by thermal processes and 9.3.A.1.ii defining cooling as 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, with 9.3.A.3.i and 9.3.A.3.ii giving the collision-level account.
• 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.

That is the entirety of what the framework says about convection: one clause of one sentence in 9.3.A.2.

Topic 9.5, Specific Heat and Thermal Conductivity, has two learning objectives, and conduction gets the second one to itself. 9.5.A concerns the energy required to change a temperature, with $Q = mc\Delta T$ at 9.5.A.1 and specific heat as an intrinsic property at 9.5.A.2. 9.5.B is to describe the rate at which energy is transferred by conduction through a given material, with 9.5.B.1 giving $Q/\Delta t = kA\Delta T/L$ and 9.5.B.2 giving thermal conductivity as an intrinsic property.

Topic 9.5 carries a boundary statement, and it is not about conduction: it reads that AP Physics 2 will model specific heat as independent of temperature, which constrains the topic's other half. Unit 9 prints three boundary statements altogether, under Topics 9.1, 9.5 and 9.6, the other two being that AP Physics 2 only expects qualitative and quantitative analysis of collisions in one and two dimensions with no functional form of the Maxwell-Boltzmann distribution required, and that only qualitative treatment of the second law of thermodynamics is within the scope of the course. Topic 9.3 carries none. So there is no boundary statement anywhere in the unit about conduction, and none about convection.

The suggested skills listed for Topic 9.3 are 1.A, 2.C, 3.B and 3.C. For Topic 9.5 they are 1.B, 2.B, 2.D, 3.A and 3.B, and the presence of 3.A, create experimental procedures that are appropriate for a given scientific question, is a hint that conduction is a plausible subject for the experimental design question, which it can be precisely because it has a measurable rate.

Topic 9.3 and Topic 9.5 carry the framing in full, and heat vs internal energy covers why all three mechanisms deliver the same kind of quantity.