热学

Matter exists in three states: solid 固体, liquid 液体 and gas 气体.

The changes of state are: melting (solid → liquid), boiling/evaporating (liquid → gas), condensation 凝结 (gas → liquid) and solidification 凝固 (liquid → solid). In condensation the gas particles slow down and come close together to form a liquid. In solidification the liquid particles lose energy and settle into fixed positions.

All matter is made of tiny particles 粒子 that are always moving. This is the kinetic particle model.

• In a solid the particles only vibrate 振动 about fixed positions.
• In a liquid they are still close but can slide past each other.
• In a gas they are far apart and move quickly in random directions.

Temperature and particle energy

When you heat a substance, its particles move faster, so they have more kinetic energy 动能. Temperature 温度 is a measure of the average kinetic energy of the particles.

The lowest possible temperature is absolute zero 绝对零度, $-273\,{}^{\circ}\text{C}$. At this point the particles have the least possible energy.

Gas pressure

Gas particles hit the walls of their container. Each hit is a tiny push. The pressure 压强 of the gas is the total force of these hits per unit area.

• Heating a gas (at constant volume) makes particles move faster and hit harder and more often, so the pressure rises.
• Squeezing a gas into a smaller volume (at constant temperature) means more hits per second on each unit of area, so the pressure rises.

For a fixed mass of gas at constant temperature:

So if the volume halves, the pressure doubles.

Worked example. A gas has a volume of $200\ \text{cm}^3$ at a pressure of $100\ \text{kPa}$. It is squeezed to $50\ \text{cm}^3$ at constant temperature. Find the new pressure.

Since $pV$ stays constant, $p_1 V_1 = p_2 V_2$:

Check the answer with a ratio: the volume became $\tfrac{1}{4}$ as big, so the pressure became $4$ times as big. You can keep cm³ and kPa here, because the same units are on both sides of the equation.

Brownian motion

If you look at smoke in air under a microscope, you see tiny specks moving in a jerky, random way. This is Brownian motion 布朗运动. The specks are pushed by fast, invisible air particles hitting them. It is strong evidence for the kinetic particle model.

The kelvin scale

Scientists often use the kelvin 开尔文 (K) temperature scale, which starts at absolute zero. To convert:

So $0\,{}^{\circ}\text{C} = 273\ \text{K}$.

Worked example. Convert $25\,{}^{\circ}\text{C}$ to kelvin, and $200\ \text{K}$ to degrees Celsius.

When matter is heated, its particles move more and take up more space, so the material expands. Gases expand the most, then liquids, then solids. This order comes from the forces between the particles: in a solid the particles are held tightly in a lattice 晶格 (a fixed pattern), so they can only vibrate a little more; in a liquid they are held less strongly; in a gas the forces are very weak, so the particles spread out much more.

Everyday examples: gaps are left between railway lines; bridges sit on rollers; a tight metal lid loosens when heated.

The internal energy 内能 of an object is the total microscopic random kinetic and potential energy of its particles, excluding the motion and position of the object as a whole. Heating an object raises its internal energy and usually its temperature.

The specific heat capacity 比热容 is the energy needed to raise the temperature of 1 kg of a material by 1 °C.

A material with a high specific heat capacity (like water) needs a lot of energy to warm up and cools down slowly.

Worked example. How much energy is needed to heat $2.0\ \text{kg}$ of water from $20\,{}^{\circ}\text{C}$ to $70\,{}^{\circ}\text{C}$? The specific heat capacity of water is $4200\ \text{J/(kg}\,{}^{\circ}\text{C)}$.

Rearranging $c = \frac{\Delta E}{m\,\Delta\theta}$ gives $\Delta E = mc\,\Delta\theta$, with $\Delta\theta = 70 - 20 = 50\,{}^{\circ}\text{C}$:

Measuring specific heat capacity. For a solid, use a metal block with two holes: one for an electric heater 加热器 and one for a thermometer 温度计. Measure the mass $m$ of the block. Switch on the heater for a measured time $t$ and record the current $I$ and the voltage $V$, so the energy supplied is $E = IVt$ (or read the energy from a joulemeter). Record the temperature rise $\Delta\theta$. Then $c = \dfrac{E}{m\,\Delta\theta}$. For a liquid, heat a measured mass of the liquid in a container and stir it, so the temperature is the same all through. Wrap the block or the container in insulating material 隔热材料, so less energy escapes to the air.

Worked example (from experimental data). A $1.0\ \text{kg}$ aluminium block is heated by a $12\ \text{V}$ heater with a current of $4.0\ \text{A}$ for $5.0$ minutes. Its temperature rises from $20\,{}^{\circ}\text{C}$ to $35\,{}^{\circ}\text{C}$. Find the specific heat capacity of aluminium.

Time in seconds: $t = 5.0 \times 60 = 300\ \text{s}$. Energy supplied:

Temperature rise: $\Delta\theta = 35 - 20 = 15\,{}^{\circ}\text{C}$.

The book value for aluminium is about $900\ \text{J/(kg}\,{}^{\circ}\text{C)}$. The measured value is too high, because some of the energy from the heater escaped to the air and did not warm the block. The calculation assumes all $14\,400\ \text{J}$ went into the block, so it gives a value that is too big. Better insulation brings the result closer.

Melting 熔化 and boiling 沸腾 need energy, but the temperature stays the same while the state changes. This energy breaks the forces between particles. For water at normal air pressure, melting is at $0\,{}^{\circ}\text{C}$ and boiling at $100\,{}^{\circ}\text{C}$.

Evaporation 蒸发 is when a liquid changes to a gas at its surface, below the boiling point. The fastest particles escape from the surface. Because the fastest (most energetic) particles leave, the average energy of those left behind falls, so the liquid cools down 冷却. An object touching an evaporating liquid also cools, because the liquid takes energy from it: this is why sweat cools your skin.

Evaporation is faster when the temperature is higher, the surface area is larger, and there is more air movement over the surface.

Worked example (reading a cooling curve). Hot liquid wax in a boiling tube is left to cool in a room at $20\,{}^{\circ}\text{C}$. A student reads its temperature every minute and plots the graph.

(a) What is the melting point of the wax? The flat part is at $69\,{}^{\circ}\text{C}$. A substance melts and solidifies at the same temperature, so the melting point is $69\,{}^{\circ}\text{C}$.

(b) What is happening between 4 and 10 minutes? The wax is solidifying: the tube holds both liquid and solid wax.

(c) Why does the temperature stay constant while energy is still being lost to the room? As the wax solidifies, its particles move closer together and are held in fixed positions by the forces between them. This releases energy, and that energy replaces the energy lost to the room, so the temperature does not fall.

(d) Why does the solid cool more slowly at the end? The wax is now closer to room temperature, so it transfers energy to the room more slowly.

Thermal energy moves from hotter places to colder places in three ways.

Conduction

Conduction 热传导 is the transfer of thermal energy through a material without the material moving. The particles in a solid sit in a lattice. Heated particles vibrate more and pass the energy to their neighbours. In metals, free electrons (delocalised electrons 自由电子) carry energy quickly, so metals are good thermal conductors 热导体.

Materials that conduct badly (like air, wood and plastic) are thermal insulators 热绝缘体.

Testing conductors. Fix a drawing pin with a little wax to one end of rods of copper, iron, glass and wood, and heat the other ends equally. The pin drops first from the copper rod, then from the iron rod, and last (or never) from the glass and the wood: metals are the best conductors. A metal rod held in a flame soon feels hot; a wooden rod does not.

Gases and most liquids are bad conductors because their particles are far apart and only pass on energy when they happen to collide. There is no lattice and there are no free electrons.

Convection

Convection 对流 happens in liquids and gases. When a fluid is heated it expands, becomes less dense, and rises. Cooler, denser fluid sinks to take its place. This circle of moving fluid is a convection current.

Showing convection. Drop a crystal of purple potassium permanganate 高锰酸钾 into a beaker of water and heat the beaker gently under the crystal. A coloured stream rises above the heat, spreads across the top and sinks at the sides. In air, a lit candle under one chimney of a smoke box pulls smoke down the other chimney and up above the flame.

Convection cannot happen in a solid because the particles cannot move from place to place.

Radiation

Thermal radiation 热辐射 is energy carried by infrared 红外线 waves. All objects emit it, and it needs no material to travel through — it can cross empty space (this is how energy reaches us from the Sun).

A surface that is dull 暗淡 and black is a good emitter 发射体 and a good absorber 吸收体 of infrared. A surface that is shiny and white is a poor emitter and a good reflector 反射体.

Comparing surfaces. Fill two cans, one dull black and one shiny silver, with hot water at the same temperature, and put a thermometer in each. The black can cools faster, so it is the better emitter. Then put the same two cans, full of cold water, at equal distances from a heater. The black can warms faster, so it is the better absorber. A Leslie cube 莱斯利立方体 (a metal box with one side of each finish) shows the same thing.

An object stays at a constant temperature when it emits energy at the same rate as it absorbs energy. The rate of emission is greater when the surface is hotter and larger. If an object absorbs energy faster than it emits it, its temperature rises; if it emits faster than it absorbs, its temperature falls.

The Earth's temperature. The Earth absorbs radiation from the Sun and emits infrared radiation back into space. Its average temperature stays constant only when the two rates are equal. Anything that changes this balance changes the temperature. Gases in the atmosphere 大气 such as carbon dioxide absorb some of the emitted infrared and send part of it back down, so more of these gases warms the Earth. Clouds and ice reflect incoming sunlight, so less ice means more energy is absorbed, and the Earth warms further.

Everyday examples

• A kitchen pan has a metal base that conducts energy quickly to the food, and a plastic or wooden handle that is an insulator, so you can hold it.
• A radiator 散热器 heats a room by convection: the air next to it warms, rises, and cooler air flows in to take its place, so the whole room warms.
• Sitting near a fire you feel its radiation on your face at once; the air between you and the fire is a poor conductor.
• A vacuum flask 保温瓶 keeps a drink hot by reducing all three transfers: the vacuum between its double walls stops conduction and convection across the gap, and its shiny silver surfaces reduce radiation. A little energy still escapes through the stopper and the neck.

• In the kinetic particle model, heating a gas makes its particles move faster and hit the walls harder and more often, so the pressure rises. The particles themselves do not get bigger.
• Evaporation happens only at the surface and at any temperature; boiling happens throughout the liquid at one fixed temperature. Evaporation cools the liquid left behind, because the fastest particles escape.
• During melting and boiling the temperature stays constant even though energy is still being supplied — that energy breaks the forces between particles.
• For specific heat capacity use $\Delta E = mc\,\Delta\theta$, where $\Delta\theta$ is the change in temperature, not the final temperature.
• Dull black surfaces are the best emitters and absorbers of infrared; shiny, light surfaces are the best reflectors. Convection needs a fluid to flow, so it cannot happen in a solid.

Common mistakes

• Using the final temperature in $\Delta E = mc\,\Delta\theta$. Use the temperature change.
• Leaving the heating time in minutes in $E = IVt$. Change it to seconds.
• Saying the particles expand when a substance is heated. The particles stay the same size; they move faster and further apart.
• Saying "no energy is supplied" on a flat part of a heating curve. Energy is still supplied; it changes the state instead of raising the temperature.
• Adding 273 to a temperature that is already in kelvin, or forgetting to add it when converting from °C.
• Saying convection happens because "heat rises". The heated fluid expands, becomes less dense and rises; cooler, denser fluid sinks.