为什么我们必须抛弃在热机中产生的额外熵?

时间:2021-11-26 22:26:39

In his introduction to thermophysics, Daniel Schroeder writes the following about the process in a heat engine:

在他对热物理学的介绍中,Daniel Schroeder在热力发动机中写下了关于过程的以下内容:

Only part of the energy absorbed as heat can be converted to work. The reason is, that the heat, as it flows in, brings along entropy, which must somehow be disposed of before the cycle can start over. To get rid of the entropy, every heat engine must dump some waste heat into its environment.

只有部分能量作为热量被吸收才能转化为能量。原因在于,热量在流入时会带来熵,在循环重新开始之前必须以某种方式处理熵。为了摆脱熵,每个热力发动机必须将一些废热排放到其环境中。

Why must the extra entropy be disposed?

为什么必须处理额外的熵?

In my understanding, we could gather more and more extra entropy, while converting all the heat into work until the entropy reaches its maximum. Then a state of equilibrium would be reached and no more energy could be withdrawn from the system according to the second law of thermodynamics. But then we could just go to the next machine and do the same, always converting all heat into work.

根据我的理解,我们可以收集越来越多的额外熵,同时将所有热量转化为工作,直到熵达到最大值。然后,根据热力学第二定律,将达到平衡状态并且不再能从系统中提取能量。但是我们可以去下一台机器做同样的事情,总是将所有的热量转化为工作。

5 个解决方案

#1


16  

We are talking about cycles here. After a complete cycle the system must be right back where it started. Since entropy is a state variable, it must then be that after one complete cycle the entropy is at its "initial" value. By the second law this must mean that the entropy has to "go somewhere else". If you "gathered more and more" entropy, then it is no longer a cycle.

我们在这里讨论周期。完成一个循环后,系统必须回到它开始的位置。由于熵是状态变量,因此必须在一个完整周期之后熵处于其“初始”值。根据第二定律,这必然意味着熵必须“去别的地方”。如果你“聚集越来越多”熵,那么它就不再是一个循环。

If you did want to do what you propose of replacing engines then it would be extremely inefficient. You would get one "run" out of the process and then have to get a new engine (I am not sure how this would actually work). It is much better to use the same engine on a cycle.

如果你确实想要做你想要更换发动机的建议那么它将是非常低效的。你会得到一个“运行”的过程,然后必须得到一个新的引擎(我不知道这将如何实际工作)。在一个循环中使用相同的引擎要好得多。

#2


5  

In my understanding, we could gather more and more extra entropy, while converting all the heat into work

根据我的理解,我们可以收集越来越多的额外熵,同时将所有的热量转化为工作

You can't store entropy while still converting all the heat into work. Storing an amount of entropy $dS$ requires that you also store an amount of energy $TdS$, where $T$ is the temperature of the object you're storing the entropy in.

在将所有热量转化为工作的同时,您无法存储熵。存储一定数量的熵$ dS $要求您还存储一定量的能量$ TdS $,其中$ T $是您存储熵的对象的温度。

But then we could just go to the next machine and do the same, always converting all heat into work.

但是我们可以去下一台机器做同样的事情,总是将所有的热量转化为工作。

You can retain some of the entropy internally inside your heat engine rather than expelling it into some external reservoir such as a river or the air. Let's say you have a tank of water that stays inside your heat engine until you throw the heat engine away. You store entropy in this tank of water, which requires heating the water. There are two issues here: (1) As the water tank gets hotter, the energy cost of storing energy in it, $TdS$, gets worse and worse. (2) The tank is no different from an external heat reservoir. You can keep it inside the box that holds your engine, but that doesn't matter. Our description of a heat engine abstracts away questions like where the low-temperature reservoir is physically located. The only real difference is that we normally idealize the low-temperature reservoir as an infinite resource, whose temperature never changes, while the tank is actually finite, and therefore worse thermodynamically because it heats up.

您可以在热力发动机内部保留一些熵,而不是将其排放到某些外部水库(如河流或空气)中。假设你有一个水箱留在你的热机内,直到你把热机扔掉。你将熵存储在这个需要加热水的水箱中。这里有两个问题:(1)随着水箱越来越热,储存能量的能源成本(TdS $)越来越差。 (2)水箱与外部蓄水池没有区别。你可以把它放在装有引擎的盒子里面,但这没关系。我们对热力发动机的描述抽象出了诸如低温油藏物理位置的问题。唯一真正的区别在于,我们通常将低温油藏理想化为无限资源,其温度从不变化,而油箱实际上是有限的,因此热力学上更糟,因为它会变热。

#3


4  

The reason you need to dump the heat is because engines, by their definition, operate in a cycle. They return to a previous configuration before continuing on. So your solution of just using an unlimited number of one-shot devices is theoretically possible. It just wouldn't be called an engine. It also wouldn't be practical. One might, however, consider the big bang itself to be the ultimate one-shot device!

您需要倾倒热量的原因是因为发动机根据其定义在一个循环中运行。在继续之前,它们将返回先前的配置。因此,理论上可以使用无限数量的一次性设备解决方案。它不会被称为引擎。它也不实用。然而,有人可能认为大爆炸本身就是最终的一次性装置!

Engines also want this cycle to go in one direction, so we have to engineer them to do so. In theory, one could have a device which simply goes in either direction without dumping heat. We've built such devices -- little turbines that operate at the molecular scale where random molecular motion causes things to bump one way or another. However, we can't make them do work (we tried). To get work out of them, we need to know which way around the cycle they will go.

发动机也希望这个循环朝着一个方向前进,所以我们必须设计它们才能这样做。从理论上讲,人们可以使用一种装置,它可以在任何方向上进行,而不会倾倒热量。我们已经建造了这样的设备 - 在分子尺度上运行的小涡轮机,其中随机分子运动导致物体以某种方式碰撞。但是,我们无法让它们发挥作用(我们尝试过)。为了解决这些问题,我们需要知道他们将走的循环方式。

To make that happen, we target two equilibrium, rather than one. One equilibrium is at maximum entropy, such as at the fullest expansion of a piston. Once we get there, we need to reset the machine, targeting a second equilibrium (such as with a piston at its most compressed). As we do this, we have to dump the heat because this second equilibrium is not the highest entropy state with all that heat in the system. We have to get rid of the heat before this second equilibrium is achieved.

为了实现这一目标,我们的目标是两个均衡,而不是一个。一个平衡处于最大熵,例如在活塞的最大膨胀处。一旦我们到达那里,我们需要重置机器,目标是第二个平衡(例如最活塞压缩的活塞)。当我们这样做时,我们必须倾倒热量,因为这个第二个平衡不是系统中所有热量的最高熵状态。在达到第二个平衡之前,我们必须摆脱热量。

Now you are allowed to use the heat to drive another engine. This is called a multi-stage engine and they are used in many power plants. They can be more efficient than a single stage engine. However, the laws of thermodynamics provide a hard limit on how efficient they can be, no matter how many stages you use. The resulting limit on efficiency is defined by Carnot's Theorem, and depends on the temperatures of the hot source and the cold sink. (Note: only heat engines have this limit. Other devices, such as fuel cells, do not operate as a heat engine, so they can achieve higher efficiency)

现在你可以用热量来驱动另一台发动机。这被称为多级发动机,它们被用于许多发电厂。它们比单级发动机更有效。然而,无论您使用多少阶段,热力学定律都会对它们的效率提供硬性限制。由此产生的效率限制由卡诺定理定义,并取决于热源和冷阱的温度。 (注意:只有热力发动机才有此限制。其他设备,如燃料电池,不作为热力发动机运行,因此它们可以实现更高的效率)

The ultimate example of this is a Matiroshka Brain. This is a fantastic megastructure wrapped around a star to get as much usable work out of the fusion engine as possible. It is a massive heat engine which has a tremendously large number of stages (thousands to millions), where the waste heat from each stage is the hot source for the next stage. The result could theoretically get close to the ultimate ideal heat engine.

最好的例子是Matiroshka Brain。这是一个奇妙的巨型结构,围绕着一颗恒星,尽可能地从融合引擎中获得尽可能多的可用工作。它是一个巨大的热力发动机,具有极大的阶段(数千到数百万),每个阶段的废热是下一阶段的热源。理论上,结果可以接近最终的理想热机。

For a Matrioshka Brain around our star (the sun), we can calculate its efficiency. The sun is roughly 5800K on its surface, so that's our hot temperature. Our low temperature is the background radiation of empty space, which is a mighty frigid 2.725. Plugging this into Carnot's equation, $\eta_{max}=1-\frac{T_C}{T_H}$, we get a maximum efficiency of 99.95%. These brains can be amazingly efficient, but they can never avoid the slow march of entropy!

对于围绕我们的恒星(太阳)的Matrioshka脑,我们可以计算它的效率。太阳表面约为5800K,这是我们的高温。我们的低温是空间的背景辐射,这是一个强大的寒冷2.725。将其插入Carnot的等式中,$ \ eta_ {max} = 1- \ frac {T_C} {T_H} $,我们得到的最大效率为99.95%。这些大脑可以非常高效,但它们永远无法避免熵的缓慢进展!

#4


0  

Single run engine, working on heat is used and known: it is rocket engine. It burn some components ( fluids, solids ) in order to obtain thrust. But it's very expensive method of going anywhere, and not so useful as you may expect. It is well designed just for it: one time run.

单一运行的发动机,使用热量并且已知:它是火箭发动机。它燃烧一些组分(流体,固体)以获得推力。但这是去任何地方的非常昂贵的方法,并没有你想象的那么有用。它专为它而设计:一次运行。

#5


0  

If you consider a structure which absorbs extra heat as part of the engine, then you can certainly make an engine which can work for a certain time without disposing of waste heat. A car engine doesn't require any cooling when it just has started, and will work for a few minutes before it overheats.

如果你考虑一种吸收额外热量的结构作为发动机的一部分,那么你当然可以制造一种可以在一定时间内工作而不会产生废热的发动机。汽车发动机刚刚启动时不需要任何冷却,并且在它过热之前会工作几分钟。

Note that the engine will not become more efficient while doing so. It will still deliver only a fraction of energy you put in as mechanical work, and the rest of the energy will be used to raise its temperature. So, your idea not improve the efficiency of the engine while drastically reducing its lifetime.

请注意,这样做时引擎不会变得更有效率。它仍然只能提供一小部分能量作为机械功,其余的能量将用于提高其温度。因此,您的想法不会提高发动机的效率,同时会大幅缩短发动机的使用寿命。

#1


16  

We are talking about cycles here. After a complete cycle the system must be right back where it started. Since entropy is a state variable, it must then be that after one complete cycle the entropy is at its "initial" value. By the second law this must mean that the entropy has to "go somewhere else". If you "gathered more and more" entropy, then it is no longer a cycle.

我们在这里讨论周期。完成一个循环后,系统必须回到它开始的位置。由于熵是状态变量,因此必须在一个完整周期之后熵处于其“初始”值。根据第二定律,这必然意味着熵必须“去别的地方”。如果你“聚集越来越多”熵,那么它就不再是一个循环。

If you did want to do what you propose of replacing engines then it would be extremely inefficient. You would get one "run" out of the process and then have to get a new engine (I am not sure how this would actually work). It is much better to use the same engine on a cycle.

如果你确实想要做你想要更换发动机的建议那么它将是非常低效的。你会得到一个“运行”的过程,然后必须得到一个新的引擎(我不知道这将如何实际工作)。在一个循环中使用相同的引擎要好得多。

#2


5  

In my understanding, we could gather more and more extra entropy, while converting all the heat into work

根据我的理解,我们可以收集越来越多的额外熵,同时将所有的热量转化为工作

You can't store entropy while still converting all the heat into work. Storing an amount of entropy $dS$ requires that you also store an amount of energy $TdS$, where $T$ is the temperature of the object you're storing the entropy in.

在将所有热量转化为工作的同时,您无法存储熵。存储一定数量的熵$ dS $要求您还存储一定量的能量$ TdS $,其中$ T $是您存储熵的对象的温度。

But then we could just go to the next machine and do the same, always converting all heat into work.

但是我们可以去下一台机器做同样的事情,总是将所有的热量转化为工作。

You can retain some of the entropy internally inside your heat engine rather than expelling it into some external reservoir such as a river or the air. Let's say you have a tank of water that stays inside your heat engine until you throw the heat engine away. You store entropy in this tank of water, which requires heating the water. There are two issues here: (1) As the water tank gets hotter, the energy cost of storing energy in it, $TdS$, gets worse and worse. (2) The tank is no different from an external heat reservoir. You can keep it inside the box that holds your engine, but that doesn't matter. Our description of a heat engine abstracts away questions like where the low-temperature reservoir is physically located. The only real difference is that we normally idealize the low-temperature reservoir as an infinite resource, whose temperature never changes, while the tank is actually finite, and therefore worse thermodynamically because it heats up.

您可以在热力发动机内部保留一些熵,而不是将其排放到某些外部水库(如河流或空气)中。假设你有一个水箱留在你的热机内,直到你把热机扔掉。你将熵存储在这个需要加热水的水箱中。这里有两个问题:(1)随着水箱越来越热,储存能量的能源成本(TdS $)越来越差。 (2)水箱与外部蓄水池没有区别。你可以把它放在装有引擎的盒子里面,但这没关系。我们对热力发动机的描述抽象出了诸如低温油藏物理位置的问题。唯一真正的区别在于,我们通常将低温油藏理想化为无限资源,其温度从不变化,而油箱实际上是有限的,因此热力学上更糟,因为它会变热。

#3


4  

The reason you need to dump the heat is because engines, by their definition, operate in a cycle. They return to a previous configuration before continuing on. So your solution of just using an unlimited number of one-shot devices is theoretically possible. It just wouldn't be called an engine. It also wouldn't be practical. One might, however, consider the big bang itself to be the ultimate one-shot device!

您需要倾倒热量的原因是因为发动机根据其定义在一个循环中运行。在继续之前,它们将返回先前的配置。因此,理论上可以使用无限数量的一次性设备解决方案。它不会被称为引擎。它也不实用。然而,有人可能认为大爆炸本身就是最终的一次性装置!

Engines also want this cycle to go in one direction, so we have to engineer them to do so. In theory, one could have a device which simply goes in either direction without dumping heat. We've built such devices -- little turbines that operate at the molecular scale where random molecular motion causes things to bump one way or another. However, we can't make them do work (we tried). To get work out of them, we need to know which way around the cycle they will go.

发动机也希望这个循环朝着一个方向前进,所以我们必须设计它们才能这样做。从理论上讲,人们可以使用一种装置,它可以在任何方向上进行,而不会倾倒热量。我们已经建造了这样的设备 - 在分子尺度上运行的小涡轮机,其中随机分子运动导致物体以某种方式碰撞。但是,我们无法让它们发挥作用(我们尝试过)。为了解决这些问题,我们需要知道他们将走的循环方式。

To make that happen, we target two equilibrium, rather than one. One equilibrium is at maximum entropy, such as at the fullest expansion of a piston. Once we get there, we need to reset the machine, targeting a second equilibrium (such as with a piston at its most compressed). As we do this, we have to dump the heat because this second equilibrium is not the highest entropy state with all that heat in the system. We have to get rid of the heat before this second equilibrium is achieved.

为了实现这一目标,我们的目标是两个均衡,而不是一个。一个平衡处于最大熵,例如在活塞的最大膨胀处。一旦我们到达那里,我们需要重置机器,目标是第二个平衡(例如最活塞压缩的活塞)。当我们这样做时,我们必须倾倒热量,因为这个第二个平衡不是系统中所有热量的最高熵状态。在达到第二个平衡之前,我们必须摆脱热量。

Now you are allowed to use the heat to drive another engine. This is called a multi-stage engine and they are used in many power plants. They can be more efficient than a single stage engine. However, the laws of thermodynamics provide a hard limit on how efficient they can be, no matter how many stages you use. The resulting limit on efficiency is defined by Carnot's Theorem, and depends on the temperatures of the hot source and the cold sink. (Note: only heat engines have this limit. Other devices, such as fuel cells, do not operate as a heat engine, so they can achieve higher efficiency)

现在你可以用热量来驱动另一台发动机。这被称为多级发动机,它们被用于许多发电厂。它们比单级发动机更有效。然而,无论您使用多少阶段,热力学定律都会对它们的效率提供硬性限制。由此产生的效率限制由卡诺定理定义,并取决于热源和冷阱的温度。 (注意:只有热力发动机才有此限制。其他设备,如燃料电池,不作为热力发动机运行,因此它们可以实现更高的效率)

The ultimate example of this is a Matiroshka Brain. This is a fantastic megastructure wrapped around a star to get as much usable work out of the fusion engine as possible. It is a massive heat engine which has a tremendously large number of stages (thousands to millions), where the waste heat from each stage is the hot source for the next stage. The result could theoretically get close to the ultimate ideal heat engine.

最好的例子是Matiroshka Brain。这是一个奇妙的巨型结构,围绕着一颗恒星,尽可能地从融合引擎中获得尽可能多的可用工作。它是一个巨大的热力发动机,具有极大的阶段(数千到数百万),每个阶段的废热是下一阶段的热源。理论上,结果可以接近最终的理想热机。

For a Matrioshka Brain around our star (the sun), we can calculate its efficiency. The sun is roughly 5800K on its surface, so that's our hot temperature. Our low temperature is the background radiation of empty space, which is a mighty frigid 2.725. Plugging this into Carnot's equation, $\eta_{max}=1-\frac{T_C}{T_H}$, we get a maximum efficiency of 99.95%. These brains can be amazingly efficient, but they can never avoid the slow march of entropy!

对于围绕我们的恒星(太阳)的Matrioshka脑,我们可以计算它的效率。太阳表面约为5800K,这是我们的高温。我们的低温是空间的背景辐射,这是一个强大的寒冷2.725。将其插入Carnot的等式中,$ \ eta_ {max} = 1- \ frac {T_C} {T_H} $,我们得到的最大效率为99.95%。这些大脑可以非常高效,但它们永远无法避免熵的缓慢进展!

#4


0  

Single run engine, working on heat is used and known: it is rocket engine. It burn some components ( fluids, solids ) in order to obtain thrust. But it's very expensive method of going anywhere, and not so useful as you may expect. It is well designed just for it: one time run.

单一运行的发动机,使用热量并且已知:它是火箭发动机。它燃烧一些组分(流体,固体)以获得推力。但这是去任何地方的非常昂贵的方法,并没有你想象的那么有用。它专为它而设计:一次运行。

#5


0  

If you consider a structure which absorbs extra heat as part of the engine, then you can certainly make an engine which can work for a certain time without disposing of waste heat. A car engine doesn't require any cooling when it just has started, and will work for a few minutes before it overheats.

如果你考虑一种吸收额外热量的结构作为发动机的一部分,那么你当然可以制造一种可以在一定时间内工作而不会产生废热的发动机。汽车发动机刚刚启动时不需要任何冷却,并且在它过热之前会工作几分钟。

Note that the engine will not become more efficient while doing so. It will still deliver only a fraction of energy you put in as mechanical work, and the rest of the energy will be used to raise its temperature. So, your idea not improve the efficiency of the engine while drastically reducing its lifetime.

请注意,这样做时引擎不会变得更有效率。它仍然只能提供一小部分能量作为机械功,其余的能量将用于提高其温度。因此,您的想法不会提高发动机的效率,同时会大幅缩短发动机的使用寿命。