《那些古怪又讓人憂心的問題》第126期:攪拌加熱(2)
(The British Felix Baumgartner)
How does stirring compare to microwaving?
那麼攪拌和微波爐加熱比起來有什麼區別呢？Based on figures from industrial mixer engineering reports, I estimate that vigorously stirring a cup of tea adds heat at a rate of about a ten-millionth of a watt. That's completely negligible.
從工業混合機工程手冊上的數字來看，我估計劇烈攪拌一杯茶增加熱能的速率約爲十萬分之一瓦。這完全可以忽略不計。
The physical effect of stirring is actually a little complicated.5 Most of the heat is carried away from teacups by the air convecting over them, and so they cool from the top down. Stirring brings fresh hot water from the depths, so it can help this process. But there are other things going on-stirring disturbs the air, and it heats the walls of the mug. It's hard to be sure what's really going on without data.
而攪拌所產生的物理效果則要複雜一些。5茶杯裏絕大多數的熱量都被茶杯上方對流的空氣帶走了，也就是說空氣使得茶從上至下冷卻。攪拌使得茶杯底部的熱水被帶到表層，因而加快了散熱的速度。但同時還發生了其他事情——攪拌也擾亂了空氣流動，使得茶杯壁溫度升高，但沒有數據，這種討論沒有太大意義。Fortunately, we have the Internet. Stack Exchange user drhodes measured the rate of teacup cooling from stirring vs. not stirring vs. repeatedly dipping a spoon into the cup vs. lifting it. Helpfully, drhodes posted both high-resolution graphs and the raw data itself, which is more than you can say for a lot of journal articles.
但別忘了我們有互聯網！StackExchange用戶drhodes恰好測量了攪拌、不攪拌、不停把勺子浸入和拿出對茶冷卻速率的影響。而且drhodes不僅上傳了高分辨率的圖像，還上傳了原始數據，這可比許多論文提供的信息有用多了。The conclusion: It doesn't really matter whether you stir, dip, or do nothing; the tea cools at about the same rate (although dipping the spoon in and out of the tea cooled it slightly faster).
結論：不管你是不停攪拌，拿勺子放進去或者乾脆啥事都不做，茶冷卻的速度都差不多。（雖然拿勺子不停放進放出能讓茶冷卻得略微快一些。）Which brings us back to the original question: Could you boil tea if you just stirred it hard enough?
於是我們又回到了最初的那個問題：我們能夠靠拼命攪拌把茶燒開嗎？No.
不能。The first problem is power. The amount of power in question, 700 watts, is about a horsepower, so if you want to boil tea in two minutes, you'll need at least one horse to stir it hard enough.
首先是因爲功率。700瓦差不多是1馬力，所以要是你想在2分鐘內把茶燒開，那麼你至少需要一匹馬幫你來拼命攪拌。You can reduce the power requirement by heating the tea over a longer period of time, but if you reduce it too far the tea will be cooling as fast as you're heating it.
當然了你可以通過延長做功時間來降低對功率的要求。只是如果時間太長的話，茶冷卻的速度就要和你加熱的速度一樣快了。Even if you could churn the spoon hard enough-tens of thousands of stirs per second-fluid dynamics would get in the way. At those high speeds, the tea would cavitate; a vacuum would form along the path of the spoon and stirring would become ineffective.6
即使你能以極高的速度攪拌——比如每秒成千上萬轉——流體力學會讓你失望的。在這種高轉速下，茶會發生空化；蒸汽泡會沿着勺子的路徑生成，此時攪拌的效率會大大下降。6And if you stir hard enough that your tea cavitates, its surface area will increase very rapidly, and it will cool to room temperature in seconds.
而如果你真的拼命攪拌到茶發生了空化，那麼它的表面溫度會急速增加，然後它會在幾秒鐘內冷卻到室溫：No matter how hard you stir your tea, it's not going to get any warmer.
不管你攪拌得多麼拼命，茶都不會變暖。1 Hydrogen and helium have a higher heat capacity by mass, but they're diffuse gasses. The only other common substance with a higher heat capacity by mass is ammonia. All three of these lose to water when measured by volume.
1． 按質量來算氫氣和氦氣有更大的比熱容，但是它們是擴散性氣體。剩下唯一一種按質量算有更大比熱容的常見物質是氨。但如果按體積算的話，這三者都比不過水。2 Note: Pushing almost-boiling water to boiling takes a large burst of extra energy on top of what's required to heat it to the boiling point - this is called the enthalpy of vaporization.
2． 注意：把即將沸騰的水加熱到煮沸狀態比把水從室溫加熱到接近煮沸的狀態需要更多的能量——這些能量叫作蒸發能。3 If they didn't, we'd just blame “inefficiency” or “vortices.”
3． 如果水不夠熱，我們就會歸咎於“效率太低”或者“渦流影響”。
