14.1 Heat

Heat and Energy Transfer

Energy transfer through heat

Heat is thermal energy that moves from a hotter object to a cooler one. This flow continues until both objects reach thermal equilibrium, the point where they share the same temperature. Energy never flows spontaneously from cold to hot.

There are three mechanisms of heat transfer:

• Conduction transfers energy through direct contact between particles. When you touch a metal spoon sitting in hot soup, the handle warms up because faster-vibrating particles at the hot end bump into their neighbors, passing kinetic energy along. The rate of conduction depends on the material's thermal conductivity. Metals conduct well; wood and air do not.
• Convection transfers energy through the bulk movement of a fluid (liquid or gas). When water heats at the bottom of a pot, that water expands, becomes less dense, and rises. Cooler, denser water sinks to replace it, creating a loop called a convection current. This is why the whole pot eventually reaches a boil, not just the bottom layer.
• Radiation transfers energy through electromagnetic waves and requires no medium at all. Sunlight warming your face is radiation traveling through the vacuum of space. Every object emits radiation depending on its temperature and surface properties. The Stefan-Boltzmann law describes the total power radiated per unit surface area of a black body: $P = \sigma A T^4$, where $\sigma$ is the Stefan-Boltzmann constant.

Conversions between heat and work

Heat and work are both ways of transferring energy, measured in the same unit: joules. James Joule's famous paddle-wheel experiment showed that a specific amount of mechanical work always produces the same amount of heat, establishing the mechanical equivalent of heat. This confirmed that heat is not a separate substance but a form of energy transfer.

The core equation connecting heat to temperature change is:

$Q = mc\Delta T$

where:

1. $Q$ = heat transferred (joules)
2. $m$ = mass of the substance (kilograms)
3. $c$ = specific heat capacity (joules per kilogram per kelvin)
4. $\Delta T$ = change in temperature (kelvins or degrees Celsius; the size of one degree is the same on both scales)

Specific heat capacity tells you how much energy it takes to raise 1 kg of a substance by 1 K. Water has a high specific heat ($c = 4{,}186 \text{ J/kg·K}$), which is why it heats up and cools down slowly compared to metals like aluminum ($c = 897 \text{ J/kg·K}$).

Effects of heat on substances

Internal energy is the total kinetic and potential energy of all the particles in a substance. Adding heat increases internal energy, usually by speeding up particle motion, which raises the temperature.

How much the temperature rises depends on the substance's specific heat capacity. Pour the same amount of energy into equal masses of water and iron, and the iron's temperature climbs much faster because its specific heat is lower.

During a phase change, a substance absorbs or releases heat without changing temperature. All the energy goes into breaking or forming bonds between particles instead of speeding them up.

• Melting (solid → liquid) requires energy input equal to the substance's latent heat of fusion. For water, that's $334{,}000 \text{ J/kg}$, which is why ice in a drink absorbs a lot of energy before it fully melts.
• Vaporization (liquid → gas) requires energy input equal to the latent heat of vaporization. For water this is $2{,}256{,}000 \text{ J/kg}$, much larger than the heat of fusion.
• Condensation (gas → liquid) releases the same amount of energy as vaporization absorbed. This is why steam burns are so dangerous: the steam dumps a huge amount of latent heat into your skin.
• Freezing (liquid → solid) releases the same amount of energy as melting absorbed.

The equation for heat during a phase change is:

$Q = mL$

where $L$ is the latent heat (of fusion or vaporization) and $m$ is the mass.

Thermodynamics and related concepts

• Thermodynamics is the study of heat, temperature, and their relationship to energy and work. The principles covered in this section feed directly into the laws of thermodynamics you'll encounter next.
• Entropy measures the disorder or randomness in a system. Natural processes tend to increase the total entropy of the universe.
• Heat capacity is the amount of heat needed to raise an entire object's temperature by one degree. It equals the specific heat capacity multiplied by the object's mass: $C = mc$.
• Thermal expansion is the tendency of matter to change in size when its temperature changes. Most materials expand when heated because their particles vibrate more and push farther apart. This is why bridges have expansion joints and why a metal lid on a glass jar loosens under hot water.