Thermodynamics
AP Physics 2 Topic 9 8:56 English narration · English + 中文 subtitles burned in
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Transcript
Put a hot cup of coffee on a table.
把一杯热咖啡放在桌上。
It always cools down. It never warms back up by taking heat out of the cool room.
它总是变凉，从不会反过来从凉爽的房间里吸热而变热。
Both directions would balance the energy books perfectly. Yet only one of them ever happens.
这两个方向在能量账上都完全说得通，但只有一个真的会发生。
Nature has a direction — and by the end of this lesson you will know why.
自然是有方向的——这节课结束时，你就会明白原因。
This is Unit Nine: thermodynamics.
这是第九单元：热力学。
Heat, temperature and energy, for a system built from billions of particles.
它研究由数十亿个粒子组成的系统中的热、温度与能量。
We start with the particles, and we finish back at that cooling cup.
我们从粒子出发，最后再回到那杯变凉的咖啡。
Let's begin.
让我们开始吧。
First, what a gas really is.
首先，气体到底是什么。
Billions of tiny particles, moving in every direction, colliding.
它是数十亿个微小粒子，朝各个方向运动、互相碰撞。
Every time one strikes a wall it gives a small push.
每当一个粒子撞上器壁，就给出一个小小的推力。
Add up those pushes and divide by the area of the wall — that is pressure.
把这些推力加起来，再除以器壁的面积，就是压强。
Heat the gas and the particles speed up: more hits, harder hits, more pressure.
给气体加热，粒子速度变快：碰撞更频繁、更用力，压强就更大。
So what is temperature?
那么温度是什么？
Kinetic theory answers it: temperature measures the average kinetic energy of the particles — three halves of the Boltzmann constant, times the absolute temperature.
温度衡量的是粒子的平均动能—— 等于二分之三倍的玻尔兹曼常量，乘以绝对温度。
Two consequences.
由此有两个结论。
Always work in kelvin, because zero kelvin is where the motion stops.
第一，永远用开尔文，因为零开尔文正是运动停止的地方。
And at the same temperature every gas has the same average kinetic energy, so a light molecule must move faster than a heavy one.
第二，在相同温度下，任何气体的平均动能都相同，所以轻分子必然比重分子运动得更快。
That is why helium leaks out of a balloon long before nitrogen does.
这就是氦气会比氮气更早从气球里漏掉的原因。
But the particles do not all move at that average.
但粒子并不都以那个平均值运动。
Plot how many particles have each speed and you get the Maxwell-Boltzmann distribution: one peak, and a long tail of very fast particles.
把「有多少粒子具有某个速率」画出来， 就得到麦克斯韦—玻尔兹曼分布：一个峰，加上一条很长的高速尾巴。
Now raise the temperature. The curve slides right and flattens.
现在提高温度，曲线向右移动并变得平坦。
The area stays the same, because the number of particles has not changed.
曲线下的面积保持不变，因为粒子数没有变化。
Exams ask you to sketch that second curve: right, lower, wider, same area.
考试常让你画出第二条曲线：向右、更低、更宽、面积相同。
Now trap the gas in a cylinder and push the piston in.
现在把气体封在气缸里，把活塞压进去。
The same particles are crowded into less space, so they reach the walls sooner and strike more often. The pressure climbs.
同样多的粒子被挤进更小的空间， 于是更快到达器壁、撞击更频繁，压强随之上升。
At a fixed temperature, halve the volume and you double the pressure.
在温度不变时，体积减半，压强就翻倍。
One equation ties it together. Pressure times volume equals the number of moles, times the gas constant, times the absolute temperature.
有一个方程把这一切联系起来：压强乘以体积，等于摩尔数乘以气体常量，再乘以绝对温度。
Count molecules instead of moles, and the Boltzmann constant takes over.
如果数的是分子个数而不是摩尔数，就换成玻尔兹曼常量。
The model assumes four things: random velocities, particles of almost no volume, perfectly elastic collisions, and no forces between collisions.
这个模型有四条假设：速度随机、粒子本身体积可忽略、碰撞完全弹性、 除碰撞之外没有作用力。
And a lovely result: plot pressure against temperature, extend the line backwards, and it reaches zero pressure at absolute zero.
还有一个漂亮的结果： 画出压强对温度的图并把直线向后延长，它会在绝对零度处达到零压强。
Let's use it.
来用一用。
A sealed rigid container holds gas at one hundred kilopascals and three hundred kelvin.
一个密封的刚性容器里装着气体，压强为一百千帕，温度为三百开尔文。
We heat it to four hundred and fifty kelvin. Find the new pressure.
把它加热到四百五十开尔文，求新的压强。
Rigid means the volume is fixed. Sealed means the amount of gas is fixed. So pressure divided by temperature stays constant.
刚性表示体积不变，密封表示气体的量不变，所以压强除以温度保持不变。
The new pressure is one hundred kilopascals, times four hundred and fifty over three hundred — one hundred and fifty kilopascals.
新的压强等于一百千帕乘以四百五十再除以三百，也就是一百五十千帕。
We never needed the volume at all.
我们完全不需要知道体积。
Two objects touch, and one is hotter.
两个物体接触，其中一个更热。
Energy in transit like this is called heat.
这样传递中的能量叫做热量。
It travels three ways: conduction through contact, convection by a moving fluid, and radiation as waves, which needs no material at all.
它有三种传递方式：靠接触的传导、靠流体流动的对流， 以及以波的形式传播、完全不需要介质的辐射。
Why always hot to cold?
为什么总是从热流向冷？
At the boundary, fast particles meet slow ones, and each collision is more likely to take energy from the fast one.
在界面处，快粒子遇上慢粒子， 每一次碰撞都更可能从快的那个身上拿走能量。
Eventually both sides sit at one temperature: thermal equilibrium, with no net transfer either way.
最终两边稳定在同一个温度：这就是热平衡，两个方向都没有净传递。
Energy is still conserved; the first law is just the bookkeeping for a gas.
能量依然守恒，第一定律只是给气体记账。
The change in internal energy equals the heat added to the gas, plus the work done on the gas.
内能的变化等于加给气体的热量，加上外界对气体做的功。
Internal energy is the total energy of the particles inside. For a monatomic ideal gas, it is three halves of the number of moles, times the gas constant, times the temperature.
内能是里面所有粒子能量的总和——对单原子理想气体， 它等于二分之三倍的摩尔数，乘以气体常量，再乘以温度。
So for an ideal gas the internal energy depends on temperature and nothing else.
所以对理想气体来说，内能只取决于温度，别的都不影响。
That is why an isothermal process has no change in internal energy.
这就是等温过程内能不变的原因。
Now the work term.
再看功这一项。
When an outside pressure changes the volume, the work done on the gas is minus that pressure, times the change in volume.
当外界压强改变气体的体积时， 外界对气体做的功等于负的压强乘以体积的变化。
Watch the signs.
注意符号。
Compress the gas, and the work done on it is positive: you push energy in.
压缩气体时，对它做的功为正：你把能量推了进去。
Let it expand, and that work is negative, because the gas spends energy pushing the world back.
让它膨胀时，这个功为负，因为气体要消耗能量把外界推开。
On a PV diagram — a pressure-volume graph — the size of that work is the area under the curve.
在压强—体积图上，这个功的大小就是曲线下的面积。
Pressure acts everywhere in the gas, not just at the walls.
压强作用在气体内部的每一点，而不只是在器壁上。
Four processes come up again and again.
有四个过程反复出现。
At constant volume nothing moves, so no work is done and every joule of heat goes into internal energy.
等容过程中什么都不动，所以不做功，每一焦耳热量都变成内能。
At constant pressure the path is flat, and the work is simply pressure times the volume change.
等压过程的路径是一条水平线，功就等于压强乘以体积的变化。
At constant temperature the path curves along an isotherm; internal energy does not change, so heat in equals work out.
等温过程的路径沿着一条等温线弯曲；内能不变，所以吸进来的热量全部变成对外做的功。
In an adiabatic process no heat enters or leaves, so an expanding gas must cool.
绝热过程中没有热量进出，所以膨胀的气体一定降温。
Whenever you sketch one, draw the direction arrow.
每次作图时，别忘了画出表示方向的箭头。
Try this one.
来试一题。
A gas takes in five hundred joules of heat. As it expands, it does two hundred joules of work on its surroundings. Find the change in its internal energy.
一份气体吸收了五百焦耳的热量，在膨胀的过程中对外界做了两百焦耳的功， 求它内能的变化。
Pause here and try it.
先暂停，自己算一算。
The gas does the work, so the work done on the gas is negative two hundred joules.
是气体在对外做功，所以外界对气体做的功是负两百焦耳。
The change in internal energy is five hundred minus two hundred: plus three hundred joules.
内能的变化等于五百减去两百，也就是增加三百焦耳。
The internal energy rose, so the gas ended up hotter.
内能上升了，所以气体最后变得更热。
How much energy does warming something up take?
把东西加热需要多少能量？
Heat equals mass, times specific heat capacity, times the temperature change.
热量等于质量，乘以比热容，再乘以温度的变化。
Specific heat is a property of the material: the energy to raise one kilogram by one degree.
比热容是材料自身的性质：把一千克升高一度所需要的能量。
Water has a huge one, about ten times copper's.
水的比热容非常大，大约是铜的十倍。
So warming two kilograms of water from twenty to eighty degrees takes five hundred thousand joules.
所以把两千克水从二十度加热到八十度，需要五十万焦耳。
That is why water cools engines, and why the sea keeps coastal cities mild.
这正是水能给发动机降温、海洋能让沿海城市气候温和的原因。
Conduction has its own equation.
热传导有自己的公式。
The rate of energy flow through a slab equals the conductivity, times the area, times the temperature difference, divided by the thickness. Four levers. A wider area is faster.
通过一块材料的能量流动速率， 等于热导率乘以面积，再乘以温度差，然后除以厚度。
A bigger temperature difference is faster. A thicker slab is slower — that is what insulation does. And the conductivity is a property of the material: high for metals, very low for still air.
这里有四个可以调的因素：面积越大越快，温差越大越快， 材料越厚越慢——保温材料正是利用这一点—— 而热导率本身是材料的性质，金属很高，静止的空气非常低。
Exams give you data and ask for a straight line, so rearrange until the gradient carries the conductivity.
考试常给你一组数据、要求画出一条直线，所以要把公式变形，让斜率里带着热导率。
One law is left, and it is the strangest.
还剩最后一条定律，也是最奇特的一条。
Entropy measures how spread out the energy is — how many ways the particles can be arranged and still look the same.
熵衡量能量分散的程度—— 也就是粒子有多少种排列方式，而整体看起来仍然一样。
There are far more ways to look like the spread-out box than the concentrated one.
看起来像右边那只「摊开」盒子的排法，远远多于左边「集中」的排法。
The second law says the total entropy of an isolated system never decreases.
热力学第二定律说：孤立系统的总熵永不减少。
Entropy depends only on the state a system is in now, not on how it got there.
熵只取决于系统此刻所处的状态，与它是怎么到达这个状态的无关。
And note the word isolated: a freezer really does lower the entropy of water, but only by pushing more entropy out into the room — the room gains more entropy than the water loses.
注意「孤立」这个词：冰箱确实降低了水的熵，但代价是把更多的熵推进房间里—— 房间增加的熵比水减少的还多。
So, back to the coffee.
现在回到那杯咖啡。
Nothing forbids the cool room from warming the cup; the energy would still balance both ways — the odds do not.
并没有哪条定律禁止凉爽的房间把杯子加热，能量账两边都平，概率却不平。
The second law is about odds.
第二定律讲的是概率。
There are vastly more ways to spread energy out than to gather it back in, so spreading always wins.
把能量摊开的方式，比把能量重新聚拢的方式多得多， 所以「摊开」总是赢。
That is why heat flows one way, why gases mix and never unmix, and why no engine can turn all of its heat into work.
这就是热量只朝一个方向流动、 气体只会混合而不会自动分开、以及没有任何热机能把热量全部变成功的原因。
Four habits that save marks.
四个能保住分数的习惯。
First, kelvin, always — a gas law fed with Celsius is simply wrong.
第一，永远用开尔文——把摄氏度代进气体定律一定是错的。
Second, the sign of the work: work done on the gas is positive, and an expanding gas gives a negative one.
第二，注意功的符号：外界对气体做功为正，气体膨胀时这个功为负。
Third, for an ideal gas the internal energy follows the temperature, and nothing else.
第三，对理想气体来说，内能只跟着温度走，别的都不影响。
Fourth, when you sketch a process, label both axes and draw the direction arrow.
第四，作图时要标出两个坐标轴，并画出表示方向的箭头。
Get those four, and this unit is yours.
做到这四点，这一单元就是你的了。