Thermal Physics
A-Level Physics Topic 14 11:46 English narration · English + 中文 subtitles burned in
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Touch a metal spoon, then a wooden table, in the same room.
在同一个房间里，先摸一把金属勺子，再摸一张木桌。
The metal feels much colder.
金属摸起来冷得多。
So it must be colder — right?
那它一定更冷——对吧？
Wrong.
错。
Bring a thermometer, and both read exactly the same temperature.
拿一支温度计来，两者读到的温度完全一样。
So why does the metal feel colder?
那金属为什么摸起来更冷？
Because your skin does not measure temperature — it measures heat flowing away.
因为你的皮肤并不测量温度——它测量热量流走的快慢。
Metal pulls heat from your hand quickly; wood barely at all.
金属很快地把热从你手上带走；木头几乎不带走。
Cold is not a thing.
冷并不是一种东西。
It is heat, leaving.
它是热在离开。
Heat and temperature are not the same thing.
热和温度并不是一回事。
Today: thermal equilibrium, the kelvin scale and absolute zero, and the energy it takes to warm and to melt.
今天：热平衡、开尔文温标与绝对零度， 以及加热和熔化所需要的能量。
Let's begin.
让我们开始吧。
Put a hot object next to a cold one, and something always happens: thermal energy flows, and it always flows one way — from the higher temperature to the lower temperature.
把一个热的物体放在一个冷的物体旁边，总会发生一件事：热能流动，而且总是朝一个方向流—— 从热到冷。
Never the other way on its own.
绝不会自己往反方向流。
It keeps flowing until both reach the same temperature.
它一直流，直到两者达到相同的温度。
Then the flow stops.
然后流动就停止了。
When two things are at the same temperature, we say they are in thermal equilibrium — balanced, with no net transfer between them.
当两个物体温度相同时，我们说它们处于热平衡——达到平衡，彼此之间没有净的能量转移。
But what is temperature, really?
但温度究竟是什么？
Zoom in, and everything is made of particles in constant, jiggling motion.
放大来看，一切都由不停地颤动着的粒子构成。
Temperature is a measure of the average kinetic energy of those particles.
温度是这些粒子平均动能的一种量度。
Hotter means they move faster; colder means they slow down.
越热，它们运动得越快；越冷，它们就越慢。
When you heat something, you are speeding up its particles.
当你加热一样东西时，你是在让它的粒子加速。
When you cool it, you are slowing them down.
当你冷却它时，你是在让它们减速。
Here is the distinction that questions are built on.
下面这个区分正是许多题目立足的地方。
Temperature decides the DIRECTION of heat flow.
温度决定的是热流的方向。
It is not a measure of how much thermal energy a body holds.
它并不是衡量一个物体含有多少热能的量度。
Compare a small cup of boiling water at one hundred degrees with a swimming pool at twenty-five degrees.
把一小杯一百度的沸水， 和一池二十五度的游泳池水比一比。
The pool holds vastly more thermal energy — far more particles, each with energy.
池水含有的热能多得多——粒子数目多得多， 每一个都带着能量。
But put a piece of metal at room temperature into the cup and it gains energy; put the same piece into the pool and it loses energy.
可是把一块室温的金属放进杯子里，它会获得能量； 把同一块金属放进泳池，它却会失去能量。
The cup is hotter, so energy flows from it; the pool holds more energy, and that is simply a different question.
杯子温度更高，所以能量从它那里流出； 而池水含有更多能量，那完全是另一个问题。
Any physical property that changes in a repeatable way with temperature can be made into a thermometer.
任何一种随温度按可重复的方式变化的物理性质，都可以做成温度计。
Four examples the syllabus names.
考纲点名了四个例子。
The volume of a liquid — a liquid-in-glass thermometer, where mercury or alcohol expands up a narrow capillary.
液体的体积——液体玻璃温度计，水银或酒精沿着细毛细管膨胀上升。
The volume, or here the pressure, of a gas — a gas thermometer, read from the height difference in a mercury manometer.
气体的体积，或者像这里一样是气体的压强——气体温度计， 从水银压力计两边的高度差读出。
The resistance of a metal — a resistance thermometer, since resistance rises nearly in step with temperature over a wide range.
金属的电阻——电阻温度计， 因为在很宽的范围内电阻几乎与温度同步上升。
And the e.m.f. of a thermocouple: two different metals joined at two points, generating an electromotive force that depends on the temperature difference between those joins.
以及热电偶的电动势： 两种不同的金属在两处连接，产生的电动势取决于这两个接点之间的温度差。
One warning: because these properties do not all change in a straight line, different thermometers can read slightly differently, and they agree exactly only at their calibration points.
有一点要注意：由于这些性质并非都按直线变化，不同的温度计读数可能略有差别， 它们只在各自的校准点上才完全一致。
The thermodynamic scale is special because it does not depend on any one substance — only on the laws of thermodynamics.
热力学温标之所以特殊，是因为它不依赖任何一种具体物质——只依赖热力学定律。
And this graph shows where its zero comes from.
而这张图显示了它的零点从何而来。
Measure a gas's pressure against Celsius temperature between nought and a hundred degrees, and the points lie on a straight line.
在零到一百摄氏度之间测量气体压强随摄氏温度的变化， 这些点落在一条直线上。
Extend it backwards and it reaches zero pressure at about minus two hundred and seventy-three degrees Celsius.
把它向后延长，它会在大约零下二百七十三摄氏度处到达零压强。
That is absolute zero: the temperature at which a system has its least possible internal energy, with essentially no random particle motion.
那就是绝对零度：系统内能取到最小可能值的温度，粒子基本上没有无规则运动。
Nothing can be cooled below it, and defining it as zero kelvin is what makes the scale absolute.
任何东西都无法被冷却到它以下，而把它定义为零开尔文，正是这个温标之所以"绝对"的原因。
To measure temperature, we use a physical property that changes with it.
要测量温度，我们利用一个随温度变化的物理性质。
A liquid expands, so a column rises.
液体会膨胀，所以液柱会上升。
A metal's resistance climbs as it warms.
金属的电阻随变热而升高。
A thermocouple makes a tiny voltage.
热电偶会产生一个微小的电压。
Any of these can be a thermometer.
这些都可以做成温度计。
But there is a deeper scale — the thermodynamic temperature scale — that does not depend on any particular substance at all.
但还有一个更深层的温标——热力学温标——它完全不依赖于任何特定的物质。
That scale is measured in kelvin.
这个温标用开尔文来量度。
It starts at the coldest temperature that can possibly exist — absolute zero, where particle motion all but stops.
它从可能存在的最冷温度开始——绝对零度，在那里粒子运动几乎停止。
There is nothing colder.
没有比它更冷的了。
To convert, just add two hundred and seventy-three point one five to a Celsius temperature.
换算时，只需在摄氏温度上加二百七十三点一五。
So zero degrees Celsius is two hundred and seventy-three kelvin; and a rise of one kelvin is exactly the same size as a rise of one degree Celsius.
所以零摄氏度是二百七十三开尔文；而升高一开尔文，和升高一摄氏度的大小完全相同。
Specific heat capacity is the energy to raise unit mass by one kelvin — c equals Q over m delta T, in joules per kilogram per kelvin.
比热容是使单位质量升高一开尔文所需的能量——c 等于 Q 除以 m delta T， 单位是焦耳每千克每开尔文。
To measure it by experiment: supply a known energy electrically from the power, using Q equals V I t, then measure the temperature rise of a known mass, and divide.
用实验测量它的办法是：用电提供已知的能量， 即 Q 等于 V I t，然后测量已知质量物体的温升，再相除。
Two practical points examiners want.
考官想看到两个实际要点。
Reduce heat loss with insulation, or lagging.
用隔热层，也就是保温包裹，来减少热损失。
And aim for a rise of about ten kelvin — big enough to measure accurately, small enough that the losses stay small.
并且把温升控制在大约十开尔文——大到足以测准，小到能让热损失保持很小。
That is the balance the question is really testing.
题目真正考的正是这个折中。
How much energy is needed to heat nought point five kilograms of water from twenty degrees Celsius to one hundred?
把零点五千克的水从二十摄氏度加热到一百摄氏度，需要多少能量？
Take the specific heat capacity of water as four thousand two hundred.
取水的比热容为四千二百。
Note the useful shortcut first: a temperature difference is the same number in kelvin and in Celsius, so delta T is simply eighty — no conversion needed here, unlike in the gas laws.
先注意那个有用的捷径： 温度差在开尔文和摄氏度里是同一个数字，所以 delta T 就是八十—— 这里不需要换算，这一点和气体定律不同。
Then Q equals m c delta T: nought point five times four thousand two hundred times eighty.
然后用 Q 等于 m c delta T： 零点五乘以四千二百再乘以八十。
That is one point six eight times ten to the fifth joules, or one hundred and sixty-eight kilojoules.
得到一点六八乘以十的五次方焦耳，也就是一百六十八千焦。
When two bodies reach equilibrium with nothing lost to the surroundings, heat lost equals heat gained.
当两个物体在没有热量散失到周围的条件下达到平衡时，放出的热等于吸收的热。
Nought point two kilograms of water at eighty degrees is mixed with nought point three kilograms at twenty degrees.
把零点二千克八十度的水与零点三千克二十度的水混合。
Find the final temperature.
求最终温度。
Since both are water, the c of water cancels from both sides straight away, which is worth spotting.
由于两边都是水，水的比热容会立刻从两边约掉，这一点值得留意。
Now set up the equation: nought point two times eighty minus T equals nought point three times T minus twenty.
现在列方程：零点二乘以八十减 T，等于零点三乘以 T 减二十。
Note the order in each bracket — the hot one is start minus final, the cold one is final minus start, so both are positive.
注意每个括号里的顺序——热的那边是初温减末温，冷的那边是末温减初温， 这样两边都是正的。
Solving gives forty-four degrees Celsius.
解出来是四十四摄氏度。
Sanity-check it: closer to twenty than to eighty, because there is more cold water than hot.
做个合理性检验： 它离二十比离八十更近，因为冷水比热水多。
How much energy does it take to heat something up?
把一样东西加热要多少能量？
That depends on its specific heat capacity — the energy to raise one kilogram by one degree.
这取决于它的比热容——把一千克升高一度所需要的能量。
Water has a huge specific heat capacity; that is why the sea warms slowly, and why water is used to cool engines.
水的比热容很大；这就是为什么海水升温缓慢，也是为什么用水来给发动机降温。
The energy needed is the mass, times the heat capacity, times the temperature rise.
所需要的能量等于质量，乘以比热容，再乘以温度的升高。
Now watch a curious thing.
现在看一件奇妙的事。
Heat ice steadily, and its temperature climbs — until it hits zero.
稳稳地给冰加热，它的温度会上升——直到升到零度。
Then, as it melts, the temperature stops rising, even though you keep adding heat.
然后，在它熔化的过程中，温度不再上升，尽管你还在不停地加热。
That hidden energy is the specific latent heat: the energy to change state, with no change in temperature.
那份隐藏的能量就是比潜热：改变状态而温度不变所需要的能量。
Melting uses the latent heat of fusion; boiling uses the latent heat of vaporisation, which is much larger.
熔化用的是熔化潜热；沸腾用的是汽化潜热，而后者要大得多。
This one graph organises the whole topic.
这一张图就把整章组织起来了。
Follow water being heated steadily.
跟着水被持续加热的过程走。
Ice warms up a slope.
冰沿着一段斜坡升温。
Then a flat plateau at zero degrees while it melts — energy going in, temperature not moving.
然后是零度处一段水平的平台，它在熔化——能量不断进去，温度却纹丝不动。
Then water warms up a steeper slope.
接着水沿着更陡的一段斜坡升温。
Then a long flat plateau at one hundred while it boils.
然后是一百度处一段很长的水平平台，它在沸腾。
Then steam warms.
最后水蒸气升温。
The rule falls straight out: on every SLOPED part you are changing temperature, so use Q equals m c delta T.
规律就直接摆在眼前：凡是倾斜的部分，你在改变温度， 就用 Q 等于 m c delta T。
On every FLAT part you are changing state at constant temperature, so use Q equals m L.
凡是水平的部分，你在恒温下改变状态，就用 Q 等于 m L。
Never mix the two — that is the commonest error in this topic.
千万不要把两者混用——那是本章最常见的错误。
And notice the boiling plateau is much longer than the melting one.
再注意，沸腾的平台比熔化的平台长得多。
Specific latent heat is the energy to change the state of unit mass at constant temperature — L equals Q over m, in joules per kilogram, with no delta T anywhere in it.
比潜热是在恒温下改变单位质量物质状态所需的能量——L 等于 Q 除以 m， 单位是焦耳每千克，式子里根本没有 delta T。
There are two kinds.
它有两种。
The specific latent heat of fusion is for melting or freezing, solid to liquid.
熔化比潜热用于熔化或凝固，即固体与液体之间。
The specific latent heat of vaporisation is for boiling or condensing, liquid to gas.
汽化比潜热用于沸腾或凝结，即液体与气体之间。
For water at atmospheric pressure, fusion is three point three four times ten to the fifth joules per kilogram, and vaporisation is two point two six times ten to the sixth — about seven times larger.
对大气压下的水来说， 熔化比潜热是三点三四乘以十的五次方焦耳每千克，汽化比潜热是二点二六乘以十的六次方—— 大约是前者的七倍。
That ratio is the length of those two plateaus on the graph.
这个比值，正是图上那两段平台的长度之比。
Why is vaporisation about seven times fusion?
汽化为什么大约是熔化的七倍？
Two reasons, and a full-mark answer gives both.
有两个原因，满分答案要把两个都说出来。
First, bonds.
第一是分子间的键。
In melting only some of the intermolecular bonds break — the particles stay close together as a liquid, just free to move past each other.
熔化时只有一部分分子间的键断开—— 粒子作为液体仍然彼此靠得很近，只是能够相互滑过。
In boiling all of them must break, so the particles can separate completely.
而沸腾时， 所有的键都必须断开，粒子才能完全分离。
Breaking all the bonds takes more energy than breaking some.
把所有的键都断开， 比只断开一部分需要更多能量。
Second, work against the atmosphere.
第二是对大气做功。
When a liquid becomes a gas it expands to roughly a thousand times the volume, and it has to push the surrounding air back to make room.
液体变成气体时， 体积膨胀到大约一千倍，它必须把周围的空气推开才腾得出地方。
That work is done using the energy you supplied.
这份功，正是用你提供的能量做的。
Multi-step problems: when one crosses a phase change, split it into stages and add the energies.
当一道题跨越了相变，就把它分成几个阶段，再把能量加起来。
Take ice at minus five degrees warming to water at thirty.
以零下五度的冰升温到三十度的水为例。
Stage one: warm the ice from minus five to zero, using m c ice times five.
第一阶段：把冰从零下五度加热到零度， 用 m 乘以冰的比热容再乘以五。
Stage two: melt it at zero, using m L f — and notice there is no delta T here, because the temperature does not move.
第二阶段：在零度熔化，用 m L f—— 注意这里没有 delta T，因为温度并不变化。
Stage three: warm the water from zero to thirty, using m c water times thirty.
第三阶段：把水从零度加热到三十度， 用 m 乘以水的比热容再乘以三十。
Add all three.
把三者相加。
The two traps are using the wrong specific heat capacity for ice versus water, and trying to put a delta T into the melting stage.
两个陷阱是：冰和水的比热容用错，以及试图在熔化那一步里塞进一个 delta T。
A two kilowatt heater boils water that is already at one hundred degrees.
一台两千瓦的加热器给已经处于一百度的水加热。
How long to turn nought point one kilograms of it into steam?
要把其中零点一千克变成水蒸气需要多久？
Because it is already at boiling point, there is no temperature change at all — so the energy needed is m L v, and nothing else.
因为它已经在沸点上，根本没有温度变化——所以所需的能量就是 m L v，别的都不用。
Nought point one times two point two six times ten to the sixth is two point two six times ten to the fifth joules.
零点一乘以二点二六乘以十的六次方，等于二点二六乘以十的五次方焦耳。
Now bring in the heater: Q equals P t, so t equals Q over P.
现在把加热器用上：Q 等于 P t，所以 t 等于 Q 除以 P。
Two point two six times ten to the fifth divided by two thousand watts gives about a hundred and ten seconds.
二点二六乘以十的五次方除以两千瓦，得到大约一百一十秒。
Three marks to secure.
三个要拿稳的分。
First, heat always flows from hot to cold, until thermal equilibrium.
第一，热总是从热流向冷，直到热平衡。
Second, convert to kelvin by adding two hundred and seventy-three — and remember, absolute zero is the limit.
第二，加上二百七十三换算成开尔文—— 并记住，绝对零度是极限。
Third, during a change of state, the temperature stays constant, because the energy goes into latent heat.
第三，在改变状态的过程中，温度保持不变，因为能量都进了潜热。
Master these, and thermal physics is yours.
掌握这些，热学就是你的了。