问与答:不稳定的气球

这为什么会发生?有两个充气气球连接管(两侧)的管哈一个水龙头,一个气球膨胀比。当我打开水龙头少的空气膨胀ballooons传递给气球充气。
——Estherika
以色列

这是一个很有趣的问题。这是我认为答案是什么。

周围的空气将的总自由能最小化空气和气球,流体流过下坡一样就可以,引力能量最小化。让我们做一些近似这种奇怪的行为是否遵循从简单的成分或需要一些特殊属性的气球。

假设空气的总量几乎是固定的。然后自由能的变化来自于拉伸的橡胶气球。假设,就像大多数有弹性的东西,多余的自由能成正比的平方他们延伸多远。现在体积会随着半径的立方,但是自由能随着半径的平方。所以过剩自由能成正比气球体积的2/3次方。的变化率对体积自由能增加(斜率或导数)就是反向与体积成正比的1/3次方。所以更加膨胀的气球增加自由能减少对于一个给定的体积增加了空气。所以自由能下降当气流从膨胀越少越膨胀的气球。这个过程将会停止膨胀的气球越少不拉伸的时候了。

迈克·W。

(发表在12/08/2007)

为什么空气从一个小气球进入大吗?谢谢你
-萨拉(37岁)
伊朗

这个旧的回答是很难找到,但我认为这是你所需要的东西。

迈克·W。

(发表在07/26/2015)

这是一个Balooney的答案。她只是问为什么流从低压到高压气球吗?答案是,没什么奇怪的!事实上,反例是正确的在实验!强大的气流和小mouth-balloon大rubber-balloon越弱。否则,如果你怀疑,大气球具有较高的压力,然后这是证明:在某一时刻两个(identically-constructed)气球都是平等的在大小和箍紧张。然后一个气球收到更多的空气,增加,拉伸,和有更多箍张力,即。在表面,更多的压力每平方英寸,这(根据帕斯卡定律)流体(空气)压力表面转移同样在空中无处不在(在气球)包括在喷嘴。现在,忘记气球大小,等等,只关注喷嘴压力。问题简化了:为什么流发生低压喷嘴的高压喷嘴吗? I suspect that the answer is that the experiment is a magic show setup, i.e., tricky. I suspect the larger balloon is of a thinner, easier stretchable material than the smaller one, hence, the smaller one is more forceful -- just as in the mouth example. In fact, when you blow air out of your mouth (such as when you cough) the air flows from a smaller mouth-balloon to a much larger atmosphere-balloon.
——匿名

严重吗?你认为空气自然流动从低到高压力?热力学的基本定律都是错了吗?

我建议你试试与普通气球。也许你会改变你的想法。

迈克·W。

(发表在01/26/2016)

不!我说的是一个完整的逆转,可能是我的表述不清楚。她是思维(即。在她看来),“流从低压到高压气球”但实际上并非如此。这是一个诡计的观察,也就是说。,其实小气球具有较高的压力。这样让我试试。(观察)流喷嘴的小气球一边的大气球。同意吗?好的。 This means there is less pressure on the large-balloon side. Agreed? OK. This means there is less pressure everywhere in the large balloon (as per Pascal's law of pressure in a static fluid). Agreed? OK. This means there is less pressure on the surface of the large balloon. Agreed? OK. This means there is less hoop tension in the large balloon skin. Agreed? OK. Assumption 1: Two balloons are identically constructed. This means the large balloon's skin is stretched less than the small balloon. Agreed? OK. This means large balloon is smaller than the small balloon. Contradiction. Hence, Assumption 1 is incorrect, i.e., two balloons are NOT identically constructed, i.e., they are magic balloons, i.e., smaller balloon's skin is stiffer than the large balloon. I then gave the example of mouth as a small balloon that inflates a large rubber balloon because mouth's skin is stiffer. Also whereas the mouth exhales into the atmosphere, hence, the mouth is a stronger balloon than the atmosphere. May be my wording was confusing. But (I think) the logic is correct. Now, my argument is based on a number of tacit assumptions. You may want to debate these assumptions: Assumption 2) Low pressure at the nozzle is the same low pressure everywhere in the large balloon -- otherwise a current would obtain which will eventually settle once the pressure equalizes everywhere. Assumption 3) Hoop tension is directly related to the internal pressure, i.e., hoop tension increases (or decreases) as does the air pressure inside. Assumption 4) As the hoop (rubber skin) tension decreases so does the surface of the balloon. This assumption is based on the elastic behavior of material -- such as the rubber skin of the balloon. Assumption 5) As the surface area decreases so does the diameter, i.e., the size of the balloon. This is just a geometry fact. So please, refute these assumption and / or the argument. Using free energy (or conservation laws) and other principles which are not directly and graphically related to the experiment leaves the questioner wanting. If you can prove your point in one way (using energy argument) you ought to be able to prove it the other way, i.e., using air pressure, hoop tension, elasticity, and so forth. Thanks.
——匿名

你的说明做了出色的清理的逻辑问题,包括你拐错了弯。我们与你到底”这意味着减少箍皮肤张力大气球。”It was that very point which we addressed indirectly in our original answer. As you say, our argument may have been too technical sounding, but you've provided a nice structure to discuss it further.

是什么压力差之间的关系在气球皮肤和气球的半径吗?就像你说的,半径变大,皮肤张力上升。紧张是如何转化为压力差吗?在平衡力在任何一小块是零。所以紧张的力量必须取消的力压差。这是关键你错过了。如果皮肤只是持平,再多的紧张局势,将创建任何力量在直角皮肤!在这个方向有一个力量的唯一原因是表面曲线,以便相邻补丁拉在一个小补丁,我们考虑。张力的力量取决于产品和曲率。是的,随着气球变大张力上升,但是曲率下降。的半径,R,曲率随着1 / R和张力的R .所以事实证明这一论点不是我们唯一的答案。

这是我们简单的论点:
1。在平衡的房间里,有一些体积V气球内的空气,在室温下。
2。假设固定体积的空气和找出如何分配,V最小化自由能。
3所示。以固定V和T V的分布没有影响空气自由能。
4所示。分布是由弹性自由能最小化的气球,fixed-total-V条件下。
这就是我们所做的。

迈克·W。

(发表在01/27/2016)

许多学生的问题或一般好学的人(比如问问题在这个论坛上,而不是那些消磨时间)是一个逻辑的解释被邪教的污染语句如“能量最小化原则”(如肥皂泡的形成)“光的最短路径。”How, do soap bubbles or light beam know calculus? That is when the studious students lose interest, because they cannot follow the line of reasoning. I wish, forums such as Physics Van and others, state assumptions and principles that are intuitive, at least as far as classical physics is concerned -- quantum confusion is another matter. So I could follow "sensibly" your statement up to your point about larger balloon has flatter surface and hence requires larger hoop tension for the same pressure. But then, that voodoo stuff about air "minimize[ing] the free energy" showed up its ugly head. That is when students lose their train of logic. If teachers (or expounders like yourself) could carry on the common-sensical explanation (at least in classical physics questions) then we mortals won't get confused. Thank you.
——匿名

谢谢你的建设性想法如何表达这些想法。这不是易事!如果我找到一个方法采取你的建议,改述我们的论点的部队没有错了,我会这样做。

你提出一个有趣的问题,这不仅适用于所有的物理,一些特殊的小类别。“如何,肥皂泡或光束知道微积分吗?”The amazing thing is that nature seems to know calculus and much fancier branches of math. In fact, it doesn't seem to know anything else.

与此同时,我认为这个不太实验,试一试自己的建议是关键!

迈克·W。

(发表在01/28/2016)

谢谢你的解释,我现在清楚实验。然而,很难吞下自然知道微积分的概念(或数学运算)。自然与(微分)立即采取行动/反应部队。全球“能量最小化”等原则的积分这些差异。事实上的完整声明上述原则是“最小化能量积分的差距。”And this requires calculus of variation -- the fancy math you alluded to. Such fancy-math based statements, are the upshot of all the millions of tedious little interactions and their primitive maths. The best, we can say is that: 'Such global (integral) statements as minimization of energy are the equivalent of pages of computation at the local (differential) level'. But now, having explicitly and formally made this (in single quotes) statement, one has to prove it. So, (at last, after this tortured thread of discussion) here is my question: Has there been any methodical program of proving each of such grandiose global statements (as the minimization of energy), for a general case, starting from the first principles (as forces, Newton's laws, etc.), in other words, changing them to theorems rather than the (present) principles? Remember a sound axiomatic system (which physics and other sciences try to be) minimizes its axioms by replacing them with theorems.
——匿名

嗯,说到公理,你根本是错误的。你写的“自然与(微分)立即采取行动/反应部队。“这是一种特定类型的当地的现实主义理论。贝尔不等式的侵犯(见如。https://van.www.chinawangyintong.com/qa/listing.php?id=30737&t=bell-inequalities)证明没有这样的理论可以描述我们的世界。

但是好吧,让我们把注意力子集的现象local-realist经典近似效果相当好。所有标准的中间力学(哈密顿和拉格朗日)是基于等价的正式证明全球原则向当地描述你提到。

在我们的气球情况下,然而,没有一个是特别相关的。我们要求什么条件的事情安定下来,没有详细的运动是什么。你所描述的小部队遵守法律,如果你反方向的时间是相同的。你有没有观察到的任何现象,都是同样的落后时间吗?我对此表示怀疑,因为这意味着所有的光线会回到太阳或者灯灯泡等等。所以如果你想问一个问题“事情安顿下来是什么样子”你绝对需要time-irreversible熵最大化原则,称为热力学第二定律。基本上说,有机会自然游荡以同样的概率通过所有可用的量子态。事实证明,绝大多数的这些国家类似,如球杯的底部,而不是滚动在边缘。所以我们预测我们将会看到的东西都是基于state-counting安顿下来,没有动力的细节。动态细节无法告诉您是否球自发地跳起来。State-counting并告诉你,大的没有,但是做的路程的。

顺便说一句,甚至在橡胶聚合物主要是由张力构型熵最大化而不是能量最小化。(和能量最小化本身是另一个更一般的熵最大化的表现。)蜷缩的聚合物有更多的选择的方法比伸长的人蜷缩被拉伸。这就是为什么在平衡你找到它们卷曲。所以即使是最mechanical-seeming方面这个问题实际上是统计。

迈克·W。

(发表在01/29/2016)