# Heat Transfer: Conduction, Convection, Radiation

Physics I · Principles of Waves, Fluids and Thermodynamics · https://tryals.app/learn/physics-i/heat-transfer-conduction-convection-radiation

## Conduction & Convection

Your skin measures heat **flow**, not temperature. Conduction, convection, and radiation are the three highways that flow takes. Engineering a thermos simply blocks all three.

**Conduction** is heat transfer via molecular collisions. Governed by **Fourier's law**:

$$\frac{dQ}{dt} = -kA\frac{dT}{dx}$$

Where $k$ is **thermal conductivity** in $W/(m \cdot K)$, $A$ is area, and $\frac{dT}{dx}$ is the temperature gradient.

For a slab of thickness $L$, we define **thermal resistance**:

$$R_{\text{th}} = \frac{L}{kA}, \quad \frac{dQ}{dt} = \frac{\Delta T}{R_{\text{th}}}$$

**Convection** is heat carried by fluid motion. Governed by Newton's law of cooling:

$$\frac{dQ}{dt} = hA(T_s - T_\infty)$$

Where $h$ is the convective heat transfer coefficient, $T_s$ is surface temperature, and $T_\infty$ is fluid temperature.

## Radiation & Thermal Rules

**Radiation** emits thermal energy via electromagnetic waves. Governed by the **Stefan-Boltzmann law**:

$$P = \varepsilon\sigma A T^4$$

| Symbol | Constant / Meaning | Value |
| --- | --- | --- |
| $\sigma$ | Stefan-Boltzmann constant | $5.67\times 10^{-8}$ W/($m^2 K^4$) |
| $\varepsilon$ | **Emissivity** | $0$ (reflector) to $1$ (blackbody) |

**Wien's displacement law** finds the peak wavelength of blackbody radiation:

$$\lambda_{\max} T = 2.898\times 10^{-3}\;\text{m K}$$

> **Physics link:** The Sun ($5778$ K) peaks at $\approx 500$ nm (visible). The Earth ($288$ K) peaks at $\approx 10\,\mu$m (infrared).

> **Common pitfall:** "Cold" does not flow into you. Heat always flows **out** from hot to cold; reversing this direction causes sign errors.

## Practice questions

8 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Complete the statement with the correct term.

**Answer:** The law describing heat conduction through a slab, Q/$t = kA \Delta T/L$, is known as **Fourier's** law.

**Why:** Fourier's law: heat flux $\propto$ thermal conductivity $k$, area $A$ and temperature gradient $\Delta T/L$.

Page: https://tryals.app/practice/physics-i/heat-transfer-conduction-convection-radiation/complete-the-statement-with-the-correct-term

### 2. Match each heat transfer mechanism to its description.

**Answer:**

- Conduction → Heat flow through a material by molecular collisions
- Convection → Heat carried by bulk fluid motion
- Radiation → Heat transferred via electromagnetic waves
- Advection → Heat transport by directed bulk fluid flow (a type of convection)

**Why:** Conduction requires direct contact, convection needs a fluid medium, radiation needs neither.

Page: https://tryals.app/practice/physics-i/heat-transfer-conduction-convection-radiation/match-each-heat-transfer-mechanism-to-its-description

### 3. Which of the following are examples of convective heat transfer?

A. Ocean currents redistributing equatorial heat
B. Boiling water circulating in a pot
C. Heat conducted along a metal rod
D. Warm air rising from a radiator heating a room

**Answer:** A. Ocean currents redistributing equatorial heat; B. Boiling water circulating in a pot; D. Warm air rising from a radiator heating a room

**Why:** Convection involves bulk fluid movement; conduction along a rod is not convection.

Page: https://tryals.app/practice/physics-i/heat-transfer-conduction-convection-radiation/which-of-the-following-are-examples-of-convective-heat-transfer

### 4. Complete the following passage by choosing the correct terms from the word bank.

**Answer:** The Stefan–Boltzmann law states that the power radiated per unit area is P/$A = \varepsilon$**σ** $T^{4}$, where $\sigma$ $\approx 5.67$ $\times 10$⁻⁸ W/($m^{2} \cdot K^{4}$) is the **Stefan–Boltzmann** constant and $\varepsilon$ is the **emissivity** of the surface.

**Why:** Stefan–Boltzmann law: $P = \varepsilon\sigma AT^{4}. A$ perfect black body has $\varepsilon$ = 1.

Page: https://tryals.app/practice/physics-i/heat-transfer-conduction-convection-radiation/complete-the-following-passage-by-choosing-the-correct-terms-from-the

### 5. Sort each example into its primary heat transfer mechanism.

**Answer:**

- Conduction: Touching a hot iron pan, Ice melting in your hand
- Convection: Wind cooling your skin
- Radiation: Sun warming Earth through space

**Why:** Direct solid contact $\to$ conduction; moving fluid $\to$ convection; EM emission without a medium $\to$ radiation.

Page: https://tryals.app/practice/physics-i/heat-transfer-conduction-convection-radiation/sort-each-example-into-its-primary-heat-transfer-mechanism

### 6. A tile floor feels much **colder** to bare feet than a wooden floor in the same room. Both floors have been in the room all night. Why the difference?

A. Tile actually is a few degrees colder than wood
B. Your feet warm the wood faster because wood is lighter
C. Tile conducts heat away from your skin faster
D. Wood generates a little heat as it slowly decomposes

**Answer:** C. Tile conducts heat away from your skin faster

**Why:** Both floors sit at room temperature; tile’s high conductivity drains heat from your sole far faster, and that flow is what "cold" feels like. Your body is a heat-flux meter, not a thermometer, the key to most "feels cold/hot" puzzles.

Page: https://tryals.app/practice/physics-i/heat-transfer-conduction-convection-radiation/a-tile-floor-feels-much-colder-to-bare-feet-than-a-wooden-floor-in

### 7. Conduction, convection and radiation transfer heat, but only one works across empty space. What distinguishes it?

A. Convection also works in a vacuum, but more slowly
B. Radiation is faster, so it crosses the gap before the vacuum matters
C. Radiation carries energy as waves and needs no matter
D. Radiation works in a vacuum because space contains a very thin medium

**Answer:** C. Radiation carries energy as waves and needs no matter

**Why:** Two mechanisms need matter and one does not. Everything the Earth receives from the Sun crosses 150 million km of vacuum, which only radiation can do.

Page: https://tryals.app/practice/physics-i/heat-transfer-conduction-convection-radiation/conduction-convection-and-radiation-transfer-heat-but-only-one

### 8. Thermal radiation can transfer heat through a vacuum because it travels as electromagnetic waves.

**Answer:** True

**Why:** Radiation requires no medium; EM waves carry energy through empty space (e.g., solar radiation reaching Earth).

Page: https://tryals.app/practice/physics-i/heat-transfer-conduction-convection-radiation/thermal-radiation-can-transfer-heat-through-a-vacuum-because-it