crumbs out of your computer keyboard , you're probably aware that after a little while,

在你的電腦鍵盤上的麵包屑 ，你可能意識到，過了一小會兒。

the air coming out of the can and even the can itself get really really cold.

從罐子裡出來的空氣，甚至罐子本身也變得非常非常冷。

Like, cold enough they put frostbite warnings on the can!

就像，冷到他們在罐子上貼上凍傷的警告!

And for good reason!

而且理由充分!

It's tempting to think that compressed air cans get cold because when the gas comes out

人們很容易認為壓縮空氣罐會變冷，因為當氣體出來時

of the can it expands and thus cools off.

它在罐子裡會膨脹，從而冷卻下來。

But that's not exactly right - whether an expanding gas gets hotter or colder (and how

但這並不完全正確--膨脹的氣體是變得更熱還是更冷（以及如何

much hotter or colder it gets) depends on the exact manner in which the gas expands.

它變得更熱或更冷）取決於氣體膨脹的確切方式。

And if we apply the relevant equation for “normal” gas expansion , we predict that

而如果我們應用 "正常 "氣體膨脹的相關方程式，我們預測

the gas inside the compressed air can should drop from room temperature to around 100 degrees

壓縮空氣罐內的氣體應從室溫降至100度左右

celsius below zero , which is, um, WAY colder than what comes out of a compressed air can.

攝氏零度以下，嗯，比壓縮空氣罐裡出來的東西要冷得多。

So the gas can't be expanding in the normal way gases expand.

所以氣體不可能以正常的氣體膨脹方式進行膨脹。

. And here's why: that would be like cutting the top off the can and letting the gas expand

.這就是原因：這就像把罐頭切掉，讓氣體膨脹。

freely in all directions.

在所有的方向上自由移動。

But the gas is actually being squeezed out through a tiny valve.

但氣體實際上是通過一個微小的閥門被擠出來的。

This difference is key; the gas passing through a valve isn't simply expanding - it's

這一區別是關鍵；通過閥門的氣體並不是簡單的膨脹--它是

also being pushed through by the rest of the gas behind it!

也被它後面的其他氣體推過!

And that compression from behind gives the gas enough heat energy to essentially counteract

而這種來自背後的壓縮給了氣體足夠的熱能，基本上可以抵消

the cooling from expansion.

膨脹帶來的冷卻。

In terms of the gas law, this means the volume goes up by the same factor that the pressure

就氣體定律而言，這意味著體積上升的因素與壓力上升的因素相同。

goes down, so pressure times volume is pretty much constant and the temperature stays about

下降，所以壓力乘以體積是基本恆定的，溫度保持在大約

constant.

恆定。

But not exactly - most gases at room temperature do get slightly colder when passing through

但並不完全如此--大多數室溫下的氣體在通過時確實會略微變冷。

a valve . A good demo of this is to let the air out of a bike tire; the valve gets colder

一個閥門。一個很好的例子是把自行車輪胎的空氣放出來；閥門會變冷。

, but not crazy cold.

，但不是瘋狂的寒冷。

Similarly, the gas leaving a can of compressed air cools a little bit passing through the

同樣地，離開壓縮空氣罐的氣體經過以下幾個方面的冷卻

nozzle . But this can't be the only contributor to the cooling.

噴嘴。但這不可能是造成冷卻的唯一因素。

I mean, the can itself cools off by significantly more than can be explained by expansion through

我的意思是，罐子本身的冷卻程度大大超過了通過膨脹所能解釋的程度。

a valve , and it's not like it's even being sprayed by the air coming out.

一個閥門，而且它甚至不像是被噴出的空氣所噴出的。

No, the real cooling power is hinted at by the warning labels on cans of compressed air

不，真正的冷卻能力是由壓縮空氣罐上的警告標籤暗示的。

telling you to not to shake them or spray them upside down - if you DO shake one, you'll

告訴你不要搖晃它們或倒過來噴 - 如果你真的搖晃它們，你會

realize right away that it's not just gas inside - there's liquid in there, too!

馬上意識到裡面不僅僅是氣體--還有液體！"。

Liquid like 1,1-difluoroethane, which is a gas at normal temperatures and pressures,

像1,1-二氟乙烷這樣的液體，在正常溫度和壓力下是一種氣體。

but a liquid once you pressurize it to around 6 times atmospheric pressure.

但一旦你把它加壓到大約6倍大氣壓，就會變成液體。

And it's the essential component of these compressed air cans.

而且它是這些壓縮空氣罐的重要組成部分。

Inside the can, 1,1-difluoroethane exists as both a liquid and a gas, in equilibrium

在罐內，1,1-二氟乙烷既是液體又是氣體，處於平衡狀態。

- just enough of the liquid boils off to maintain six atmospheres of pressure in the top of

- 剛好有足夠的液體沸騰出來，以保持在頂部的六個大氣壓的壓力。

the can, a pressure high enough that rest stays liquid.

罐子裡的壓力足夠高，以便其餘部分保持液體狀態。

Because it's at six times atmospheric pressure, when you open the valve the difluoroethane

因為它的壓力是大氣壓的六倍，當你打開閥門時，二氟乙烷

rushes out in a steady stream.

源源不斷地衝出來。

But this then means that the inside of the can is no longer pressurized enough to keep

但這意味著罐子內部不再有足夠的壓力來保持

the liquid from boiling - so more of it boils off until the gas reaches six atmospheres

液體不會沸騰--是以更多的液體會沸騰，直到氣體達到六個大氣壓。

of pressure again and a new equilibrium is reached with slightly less liquid in the can.

再次加壓，達到新的平衡，罐內液體略少。

This is how the can is able to keep blowing a stream of consistent strength even when

這就是為什麼罐子能夠持續吹出穩定的強度，即使在

mostly empty.

大部分是空的。

But more importantly to our temperature conundrum, changes from liquid phase to gas phase require

但對我們的溫度難題更重要的是，從液相到氣相的變化需要

a TON of energy, and that energy has to come from somewhere.

大量的能量，而這些能量必須來自某處。

Just like how the evaporation of sweat removes energy from your skin, cooling you off, inside

就像汗水的蒸發如何從你的皮膚上帶走能量，使你冷卻下來一樣，在內部

a can of compressed air, vaporization - aka boiling - is what steals energy from the liquid

在一罐壓縮空氣中，汽化--又稱沸騰--是從液體中竊取能量的。

and cools it off.

並將其冷卻。

Significantly!

顯著的!

Spraying out 10% of the contents will cool the entire remainder of the can by around

噴出10%的內容物將使整個罐子的剩餘部分冷卻約10分鐘。

20 degrees celsius!

攝氏20度!

If it seems counterintuitive that a boiling substance cools itself off, look no further

如果沸騰的物質會自行冷卻，這似乎有悖常理，那就不要再看了

than the humble pressure cooker . Water normally boils above 100 degrees celsius, but by sealing

比起簡陋的快鍋，壓力鍋.水通常會在100攝氏度以上沸騰，但通過密封

in steam, the pressure rises, enabling the water in the pot to remain a liquid well beyond

在蒸汽中，壓力上升，使鍋裡的水保持液體狀態，遠遠超過了水的溫度。

water's normal boiling point - just like the difluoroethane in a can of compressed

水的正常沸點--就像一罐壓縮空氣中的二氟乙烷。

air.

空氣。

And releasing water vapor out of the nozzle of a pressure cooker lowers the pressure inside,

而將水蒸氣從壓力鍋的噴嘴中釋放出來會降低內部的壓力。

allowing a bit more water to boil off as steam and lowering the temperature of the remaining

讓更多的水作為蒸汽沸騰，並降低剩餘的溫度。

water - just like the difluoroethane in a compressed air can.

水 - 就像壓縮空氣罐中的二氟乙烷。

And if you keep letting off steam, eventually the water will cool all the way back down

而如果你繼續放出蒸汽，最終水會一路冷卻下來。

to its regular boiling point of 100 degrees , just like how if you keep spraying a can

到100度的常規沸點，就像你不斷噴灑一罐

of compressed air, the difluoroethane inside will cool all the way back down to its regular

在壓縮空氣的作用下，裡面的二氟乙烷會一直冷卻到其正常狀態。

boiling point of negative 25 degrees .

沸點為負25度。

A can of compressed air is quite literally a 1,1-difluoroethane pressure cooker.

一罐壓縮空氣簡直就是一個1,1-二氟乙烷壓力鍋。

And just like you shouldn't shake a pressure cooker or turn it upside down (unless you

就像你不應該搖晃快鍋，壓力鍋或把它倒過來一樣（除非你

want to spray superheated water everywhere), cans of compressed air don't work very well

想把過熱的水噴得到處都是），壓縮空氣罐的效果不是很好。

sideways or upside down: instead of spraying out gas, you'll spray out the liquid that

側面或顛倒：你不是噴出氣體，而是噴出液體，而不是噴出氣體。

was only being kept liquified by the high pressure inside the can , so it immediately

只有通過罐內的高壓才能保持液化，是以它立即

vaporizes and drastically cools down whatever it's contacting . INSTANT ICE! (though difluoroethane

蒸發並大幅冷卻它所接觸到的東西。瞬間結冰！（儘管二氟乙烷

can dissolve in water and is poisonous, so definitely don't use this ice for anything

可以溶解於水，並且有毒，所以絕對不要用這種冰塊做任何事情。

food-related).

與食品有關）。)

In conclusion, the cause for the coldness of cans of compressed air can be clarified

綜上所述，可以明確壓縮空氣罐的冷度原因

by comprehending the consequent clue: they aren't actually cans of compressed air.

通過理解隨之而來的線索：它們實際上並不是壓縮空氣的罐子。

They're cans of pressure-liquified 1,1-difluoroethane, and lowering the pressure inside by spraying

它們是一罐加壓液化的1,1-二氟乙烷，通過噴灑來降低內部壓力。

them allows more liquid to boil off, cooling what remains.

它們允許更多的液體沸騰，冷卻剩下的液體。

I love learning about the physics of regular stuff; I mean, black holes and quantum mechanics

我喜歡學習常規的物理學知識；我是說，黑洞和量子力學

are cool, too, but they're not quite as tangible or relatable as the things we interact

也很酷，但它們並不像我們互動的東西那樣有形或可親。

with on a regular basis.

偶爾也會與之合作。

And if you, too, want to dive deeper into the physics of everyday objects, look no further

如果你也想更深入地研究日常物品的物理學，就不要再看了

than Brilliant, this video's sponsor.

比起Brilliant，這個視頻的贊助商。

Brilliant has a whole course on the physics of everyday objects, including fridges and

Brilliant有一門關於日常物品的物理學課程，包括冰箱和水壺。

water towers and bikes - bikes are great! - and Brilliant also has fun, short daily

水塔和自行車--自行車是很好的!- 輝煌也有有趣的、簡短的日常

challenges and puzzles to learn about stuff like regression to the mean and fluids and

挑戰和謎題，以瞭解諸如迴歸平均值和流體和的東西。

thermodynamics without the huge time commitment it would take to learn enough about Joule-Thompson

熱力學，而不需要花費大量的時間來學習足夠的焦耳-湯普森知識。

expansion through a valve to make a whole youtube video about it…

擴張通過一個閥門，使整個YouTube視頻關於它...

Brilliant continues to be an incredible supporter of MinutePhysics and they're offering 20%

百利公司繼續是MinutePhysics的一個令人難以置信的支持者，他們正在提供20%的優惠。

off of a premium subscription to the first 200 of you who go to brilliant.org/minutephysics,

對前200名進入brilliant.org/minutephysics的人提供高級訂閱的優惠。

which gives you full access to all of Brilliant's courses, puzzles and daily challenges.

這使你可以完全進入Brilliant的所有課程、謎題和每日挑戰。

Again, that's brilliant.org/minutephysics for 20% off a premium subscription, and to

同樣，這也是brilliant.org/minutephysics，可獲得高級訂閱的八折優惠，並可前往

let Brilliant know you came from here.

讓Brilliant知道你來自這裡。