[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.10,0:00:02.14,Default,,0000,0000,0000,,我們來多做點題吧
Dialogue: 0,0:00:02.14,0:00:04.56,Default,,0000,0000,0000,,關於理想氣體物態方程的題目
Dialogue: 0,0:00:04.56,0:00:06.68,Default,,0000,0000,0000,,假設我有一罐氣體
Dialogue: 0,0:00:06.68,0:00:15.32,Default,,0000,0000,0000,,當前壓力是3個大氣壓
Dialogue: 0,0:00:15.32,0:00:19.76,Default,,0000,0000,0000,,假設罐子的體積是
Dialogue: 0,0:00:19.76,0:00:27.41,Default,,0000,0000,0000,,比如 9升
Dialogue: 0,0:00:27.41,0:00:30.14,Default,,0000,0000,0000,,現在 氣壓會如何改變
Dialogue: 0,0:00:30.14,0:00:39.28,Default,,0000,0000,0000,,如果體積從9升變爲3升
Dialogue: 0,0:00:39.28,0:00:42.18,Default,,0000,0000,0000,,從第一個理想氣體物態方程的影片中
Dialogue: 0,0:00:42.18,0:00:43.35,Default,,0000,0000,0000,,你可以大概感覺到
Dialogue: 0,0:00:43.35,0:00:46.94,Default,,0000,0000,0000,,如果你有一堆——保持——
Dialogue: 0,0:00:46.94,0:00:47.90,Default,,0000,0000,0000,,這很重要
Dialogue: 0,0:00:47.90,0:00:50.76,Default,,0000,0000,0000,,我們保持溫度不變
Dialogue: 0,0:00:50.76,0:00:52.54,Default,,0000,0000,0000,,這很重要 必須明白
Dialogue: 0,0:00:52.54,0:00:58.38,Default,,0000,0000,0000,,所以在我們的直覺
Dialogue: 0,0:00:58.38,0:01:00.35,Default,,0000,0000,0000,,在理想氣體物態方程背後 我們說
Dialogue: 0,0:01:00.35,0:01:02.99,Default,,0000,0000,0000,,看 如果我們有一定量的粒子
Dialogue: 0,0:01:02.99,0:01:06.85,Default,,0000,0000,0000,,以及一定的動能
Dialogue: 0,0:01:06.85,0:01:08.83,Default,,0000,0000,0000,,他們施加一定的壓力
Dialogue: 0,0:01:08.83,0:01:09.78,Default,,0000,0000,0000,,在容器壁上
Dialogue: 0,0:01:09.78,0:01:14.37,Default,,0000,0000,0000,,如果我們要讓容器變小
Dialogue: 0,0:01:14.37,0:01:16.20,Default,,0000,0000,0000,,我們有同樣數量的粒子
Dialogue: 0,0:01:16.20,0:01:17.43,Default,,0000,0000,0000,,n不變
Dialogue: 0,0:01:17.43,0:01:19.88,Default,,0000,0000,0000,,平均動能不變
Dialogue: 0,0:01:19.88,0:01:21.66,Default,,0000,0000,0000,,所以它們會更頻繁地撞上容器壁
Dialogue: 0,0:01:21.66,0:01:24.22,Default,,0000,0000,0000,,所以當我們使容器縮小時
Dialogue: 0,0:01:24.22,0:01:26.73,Default,,0000,0000,0000,,當體積變大
Dialogue: 0,0:01:26.73,0:01:27.76,Default,,0000,0000,0000,,當體積變小時
Dialogue: 0,0:01:27.76,0:01:30.07,Default,,0000,0000,0000,,氣壓應該升高
Dialogue: 0,0:01:30.07,0:01:32.62,Default,,0000,0000,0000,,所以我們看看能不能算出準確數字
Dialogue: 0,0:01:32.62,0:01:35.43,Default,,0000,0000,0000,,我們可以用理想氣體方程了
Dialogue: 0,0:01:35.43,0:01:41.87,Default,,0000,0000,0000,,壓力乘體積等於nRT
Dialogue: 0,0:01:41.87,0:01:44.32,Default,,0000,0000,0000,,現在 粒子數改變了嗎
Dialogue: 0,0:01:44.32,0:01:47.98,Default,,0000,0000,0000,,在我改變情況縮小了體積時？
Dialogue: 0,0:01:47.98,0:01:48.65,Default,,0000,0000,0000,,不！
Dialogue: 0,0:01:48.65,0:01:49.76,Default,,0000,0000,0000,,我們有一樣的粒子數
Dialogue: 0,0:01:49.76,0:01:50.92,Default,,0000,0000,0000,,我只是把容器縮小了
Dialogue: 0,0:01:50.92,0:01:55.20,Default,,0000,0000,0000,,所以n還是n R不變 那是個常數
Dialogue: 0,0:01:55.20,0:01:57.22,Default,,0000,0000,0000,,溫度不變
Dialogue: 0,0:01:57.22,0:02:00.32,Default,,0000,0000,0000,,所以我原先的壓力乘體積
Dialogue: 0,0:02:00.32,0:02:02.69,Default,,0000,0000,0000,,等於nRT
Dialogue: 0,0:02:02.69,0:02:04.31,Default,,0000,0000,0000,,而我的新壓力乘體積——
Dialogue: 0,0:02:04.31,0:02:07.95,Default,,0000,0000,0000,,讓我叫這個P1和V1
Dialogue: 0,0:02:07.95,0:02:11.00,Default,,0000,0000,0000,,然後P2是這個
Dialogue: 0,0:02:11.00,0:02:15.60,Default,,0000,0000,0000,,不好意思 那是V2
Dialogue: 0,0:02:15.60,0:02:21.70,Default,,0000,0000,0000,,所以V2是這個 我們要算出P2
Dialogue: 0,0:02:21.70,0:02:23.13,Default,,0000,0000,0000,,P2是什麽？
Dialogue: 0,0:02:23.13,0:02:31.35,Default,,0000,0000,0000,,我們知道P1乘V1等於nRT
Dialogue: 0,0:02:31.35,0:02:33.40,Default,,0000,0000,0000,,我們還知道既然氣體的溫度和
Dialogue: 0,0:02:33.40,0:02:35.98,Default,,0000,0000,0000,,莫耳數都不變
Dialogue: 0,0:02:35.98,0:02:40.79,Default,,0000,0000,0000,,P2乘V2等於nRT
Dialogue: 0,0:02:40.79,0:02:43.20,Default,,0000,0000,0000,,既然它們都等於同一個東西
Dialogue: 0,0:02:43.20,0:02:45.67,Default,,0000,0000,0000,,我們可以說壓力乘體積
Dialogue: 0,0:02:45.67,0:02:47.80,Default,,0000,0000,0000,,只要溫度不變
Dialogue: 0,0:02:47.80,0:02:49.20,Default,,0000,0000,0000,,就也不變
Dialogue: 0,0:02:49.20,0:02:55.76,Default,,0000,0000,0000,,所以P1乘V1也等於P2乘V2
Dialogue: 0,0:02:55.76,0:02:57.94,Default,,0000,0000,0000,,那P1是什麽？
Dialogue: 0,0:02:57.94,0:03:03.23,Default,,0000,0000,0000,,P1 我們原先的壓力 是3個大氣壓
Dialogue: 0,0:03:06.63,0:03:12.02,Default,,0000,0000,0000,,所以3大氣壓乘9升等於
Dialogue: 0,0:03:12.02,0:03:15.98,Default,,0000,0000,0000,,我們的新氣壓乘3升
Dialogue: 0,0:03:15.98,0:03:18.99,Default,,0000,0000,0000,,如果我們將等式兩邊同除以3
Dialogue: 0,0:03:18.99,0:03:24.70,Default,,0000,0000,0000,,3升就消掉了
Dialogue: 0,0:03:24.70,0:03:33.64,Default,,0000,0000,0000,,我們還有9大氣壓
Dialogue: 0,0:03:33.64,0:03:34.80,Default,,0000,0000,0000,,這有道理
Dialogue: 0,0:03:34.80,0:03:39.26,Default,,0000,0000,0000,,當你把體積縮小2/3
Dialogue: 0,0:03:39.26,0:03:40.30,Default,,0000,0000,0000,,或者當你使體積
Dialogue: 0,0:03:40.30,0:03:42.94,Default,,0000,0000,0000,,變爲原來的1/3
Dialogue: 0,0:03:42.94,0:03:46.20,Default,,0000,0000,0000,,你的壓力就會增加3倍
Dialogue: 0,0:03:46.20,0:03:51.57,Default,,0000,0000,0000,,所以這個乘3 這個乘1/3
Dialogue: 0,0:03:51.57,0:03:52.90,Default,,0000,0000,0000,,一般這是很有用的知識
Dialogue: 0,0:03:52.90,0:03:55.20,Default,,0000,0000,0000,,如果溫度不變
Dialogue: 0,0:03:55.20,0:03:57.48,Default,,0000,0000,0000,,那麽壓力乘體積
Dialogue: 0,0:03:57.48,0:03:59.11,Default,,0000,0000,0000,,也是一個常數
Dialogue: 0,0:03:59.11,0:04:00.96,Default,,0000,0000,0000,,現在 你可以更進一步
Dialogue: 0,0:04:00.96,0:04:06.88,Default,,0000,0000,0000,,如果我們看看PV＝nRT
Dialogue: 0,0:04:06.88,0:04:09.16,Default,,0000,0000,0000,,我們知道兩個量不變
Dialogue: 0,0:04:09.16,0:04:11.84,Default,,0000,0000,0000,,在我們做的大部分練習中
Dialogue: 0,0:04:11.84,0:04:13.54,Default,,0000,0000,0000,,就是分子數
Dialogue: 0,0:04:13.54,0:04:15.53,Default,,0000,0000,0000,,以及顯然R不會變
Dialogue: 0,0:04:15.53,0:04:18.26,Default,,0000,0000,0000,,所以如果我們將兩邊同除以T
Dialogue: 0,0:04:18.26,0:04:23.16,Default,,0000,0000,0000,,我們就有了PV/T＝nR
Dialogue: 0,0:04:23.16,0:04:24.92,Default,,0000,0000,0000,,或者可以說它等於一個常數
Dialogue: 0,0:04:24.92,0:04:27.20,Default,,0000,0000,0000,,它對於任何係統都是一個常數
Dialogue: 0,0:04:27.20,0:04:28.63,Default,,0000,0000,0000,,如果我們不改變
Dialogue: 0,0:04:28.63,0:04:31.52,Default,,0000,0000,0000,,容器中的分子數的話
Dialogue: 0,0:04:31.52,0:04:33.37,Default,,0000,0000,0000,,所以 如果我們改變壓力——
Dialogue: 0,0:04:33.37,0:04:35.65,Default,,0000,0000,0000,,如果一開始有
Dialogue: 0,0:04:35.65,0:04:40.00,Default,,0000,0000,0000,,壓力1 體積1 以及某個溫度1
Dialogue: 0,0:04:40.00,0:04:41.50,Default,,0000,0000,0000,,那就等於這個常數
Dialogue: 0,0:04:41.50,0:04:44.19,Default,,0000,0000,0000,,如果我們改變其中一個
Dialogue: 0,0:04:44.19,0:04:44.73,Default,,0000,0000,0000,,我們回到
Dialogue: 0,0:04:44.73,0:04:48.86,Default,,0000,0000,0000,,壓力2 體積2 溫度2
Dialogue: 0,0:04:48.86,0:04:50.47,Default,,0000,0000,0000,,他們應該還等於這個常數
Dialogue: 0,0:04:50.47,0:04:51.47,Default,,0000,0000,0000,,所以他們相等
Dialogue: 0,0:04:51.47,0:04:55.35,Default,,0000,0000,0000,,舉例來說 假設我開始有
Dialogue: 0,0:04:55.35,0:05:01.08,Default,,0000,0000,0000,,1個大氣壓的壓力
Dialogue: 0,0:05:01.08,0:05:05.07,Default,,0000,0000,0000,,而體積是——
Dialogue: 0,0:05:05.07,0:05:08.61,Default,,0000,0000,0000,,我換一下單位來試一種不同的做法
Dialogue: 0,0:05:08.61,0:05:10.64,Default,,0000,0000,0000,,——2立方米
Dialogue: 0,0:05:10.64,0:05:20.21,Default,,0000,0000,0000,,假設溫度是27攝氏度
Dialogue: 0,0:05:20.21,0:05:21.74,Default,,0000,0000,0000,,我剛寫了攝氏度
Dialogue: 0,0:05:21.74,0:05:22.70,Default,,0000,0000,0000,,以爲我想讓你永遠記住
Dialogue: 0,0:05:22.70,0:05:23.97,Default,,0000,0000,0000,,你要轉換成開氏度
Dialogue: 0,0:05:23.97,0:05:27.83,Default,,0000,0000,0000,,所以27攝氏度加上273是
Dialogue: 0,0:05:27.83,0:05:33.15,Default,,0000,0000,0000,,正好300開氏度
Dialogue: 0,0:05:33.15,0:05:39.53,Default,,0000,0000,0000,,我們的新溫度是
Dialogue: 0,0:05:39.53,0:05:40.63,Default,,0000,0000,0000,,實際上我們來算一下新溫度
Dialogue: 0,0:05:40.63,0:05:41.42,Default,,0000,0000,0000,,會是什麽
Dialogue: 0,0:05:41.42,0:05:46.27,Default,,0000,0000,0000,,假設新壓力是2大氣壓
Dialogue: 0,0:05:46.27,0:05:47.88,Default,,0000,0000,0000,,壓力增加了
Dialogue: 0,0:05:47.88,0:05:50.01,Default,,0000,0000,0000,,我們讓容器縮小
Dialogue: 0,0:05:50.01,0:05:52.49,Default,,0000,0000,0000,,比如1立方米
Dialogue: 0,0:05:52.49,0:05:55.10,Default,,0000,0000,0000,,所以容器縮小了一半
Dialogue: 0,0:05:55.10,0:05:56.68,Default,,0000,0000,0000,,而壓力增加了一半
Dialogue: 0,0:05:56.68,0:05:57.59,Default,,0000,0000,0000,,所以你可以猜一下
Dialogue: 0,0:05:57.59,0:06:02.15,Default,,0000,0000,0000,,你知道我們讓壓力升高了
Dialogue: 0,0:06:02.15,0:06:08.18,Default,,0000,0000,0000,,我來讓容器更小一點
Dialogue: 0,0:06:08.18,0:06:08.77,Default,,0000,0000,0000,,實際上 算了
Dialogue: 0,0:06:08.77,0:06:10.71,Default,,0000,0000,0000,,我來讓壓力更大
Dialogue: 0,0:06:10.71,0:06:14.26,Default,,0000,0000,0000,,讓壓力變成5個大氣壓
Dialogue: 0,0:06:14.26,0:06:16.94,Default,,0000,0000,0000,,現在我們想知道第二個溫度是什麽
Dialogue: 0,0:06:16.94,0:06:18.81,Default,,0000,0000,0000,,我們建立起等式
Dialogue: 0,0:06:18.81,0:06:19.53,Default,,0000,0000,0000,,所以就得到
Dialogue: 0,0:06:19.53,0:06:28.10,Default,,0000,0000,0000,,2/300大氣壓乘立方米每開氏度
Dialogue: 0,0:06:28.10,0:06:32.69,Default,,0000,0000,0000,,等於2/T2 我們的新溫度
Dialogue: 0,0:06:32.69,0:06:40.15,Default,,0000,0000,0000,,然後我們有1500等於2T2
Dialogue: 0,0:06:40.15,0:06:41.37,Default,,0000,0000,0000,,兩邊同除以2
Dialogue: 0,0:06:41.37,0:06:46.90,Default,,0000,0000,0000,,得到了T2等於750開氏度
Dialogue: 0,0:06:46.90,0:06:48.31,Default,,0000,0000,0000,,這有道理 對吧
Dialogue: 0,0:06:48.31,0:06:50.54,Default,,0000,0000,0000,,我們讓壓力升高了這麽多
Dialogue: 0,0:06:50.54,0:06:53.29,Default,,0000,0000,0000,,而同時也減小了體積
Dialogue: 0,0:06:53.29,0:06:55.64,Default,,0000,0000,0000,,所以溫度必須擧升
Dialogue: 0,0:06:55.64,0:06:56.55,Default,,0000,0000,0000,,或者如果這麽想
Dialogue: 0,0:06:56.55,0:06:58.18,Default,,0000,0000,0000,,或許我們升高了溫度
Dialogue: 0,0:06:58.18,0:06:59.50,Default,,0000,0000,0000,,因此也使壓力
Dialogue: 0,0:06:59.50,0:07:00.69,Default,,0000,0000,0000,,變得高多了
Dialogue: 0,0:07:00.69,0:07:03.87,Default,,0000,0000,0000,,尤其是當我們減小了體積時
Dialogue: 0,0:07:03.87,0:07:05.40,Default,,0000,0000,0000,,我想最好的理解方法是
Dialogue: 0,0:07:05.40,0:07:08.23,Default,,0000,0000,0000,,壓力升高了這麽多
Dialogue: 0,0:07:08.23,0:07:10.20,Default,,0000,0000,0000,,它增加了五倍
Dialogue: 0,0:07:10.20,0:07:12.48,Default,,0000,0000,0000,,他從1大氣壓變爲5大氣壓
Dialogue: 0,0:07:12.48,0:07:14.37,Default,,0000,0000,0000,,因爲一面
Dialogue: 0,0:07:14.37,0:07:18.03,Default,,0000,0000,0000,,我們將體積縮小了1/2
Dialogue: 0,0:07:18.03,0:07:19.68,Default,,0000,0000,0000,,所以壓力應該加倍了
Dialogue: 0,0:07:19.68,0:07:21.90,Default,,0000,0000,0000,,我們就到了2大氣壓
Dialogue: 0,0:07:21.90,0:07:23.78,Default,,0000,0000,0000,,然後我們讓溫度高多了
Dialogue: 0,0:07:23.78,0:07:25.41,Default,,0000,0000,0000,,所以我們也在撞上容器壁
Dialogue: 0,0:07:25.41,0:07:27.90,Default,,0000,0000,0000,,我們使溫度變爲750開氏度
Dialogue: 0,0:07:27.90,0:07:29.89,Default,,0000,0000,0000,,所以溫度升高了兩倍還多
Dialogue: 0,0:07:29.89,0:07:33.88,Default,,0000,0000,0000,,於是我們得到了5大氣壓
Dialogue: 0,0:07:33.88,0:07:37.99,Default,,0000,0000,0000,,現在 另一件你可能會聽到的概念
Dialogue: 0,0:07:37.99,0:07:39.69,Default,,0000,0000,0000,,是發生什麽
Dialogue: 0,0:07:39.69,0:07:42.48,Default,,0000,0000,0000,,在標準溫度和氣壓下
Dialogue: 0,0:07:42.48,0:07:44.04,Default,,0000,0000,0000,,我把這些都刪了
Dialogue: 0,0:07:44.04,0:07:47.57,Default,,0000,0000,0000,,標準溫度和氣壓
Dialogue: 0,0:07:47.57,0:07:51.53,Default,,0000,0000,0000,,我把這些不需要的都刪掉
Dialogue: 0,0:07:52.89,0:07:56.81,Default,,0000,0000,0000,,標準溫度和氣壓
Dialogue: 0,0:07:56.81,0:07:57.47,Default,,0000,0000,0000,,我提到這個
Dialogue: 0,0:07:57.47,0:07:58.69,Default,,0000,0000,0000,,是因爲雖然它被稱作
Dialogue: 0,0:07:58.69,0:07:59.88,Default,,0000,0000,0000,,標準溫度和氣壓
Dialogue: 0,0:07:59.88,0:08:03.70,Default,,0000,0000,0000,,有時也稱作STP
Dialogue: 0,0:08:03.70,0:08:05.74,Default,,0000,0000,0000,,世界的一大不幸是
Dialogue: 0,0:08:05.74,0:08:07.84,Default,,0000,0000,0000,,人們還沒有完全標準化
Dialogue: 0,0:08:07.84,0:08:13.74,Default,,0000,0000,0000,,標準氣壓和溫度是什麽
Dialogue: 0,0:08:13.74,0:08:15.92,Default,,0000,0000,0000,,我在維基百科上查了一下
Dialogue: 0,0:08:15.92,0:08:16.88,Default,,0000,0000,0000,,你可能會看到的
Dialogue: 0,0:08:16.88,0:08:19.99,Default,,0000,0000,0000,,在大部分物理課以及標準化考試上的
Dialogue: 0,0:08:19.99,0:08:23.94,Default,,0000,0000,0000,,標準溫度是0攝氏度
Dialogue: 0,0:08:23.94,0:08:26.84,Default,,0000,0000,0000,,也就是 當然 273開氏度
Dialogue: 0,0:08:26.84,0:08:30.30,Default,,0000,0000,0000,,標準氣壓是1個大氣壓
Dialogue: 0,0:08:30.30,0:08:31.24,Default,,0000,0000,0000,,在維基百科上
Dialogue: 0,0:08:31.24,0:08:38.53,Default,,0000,0000,0000,,他們寫成101.325千帕斯卡
Dialogue: 0,0:08:38.53,0:08:41.34,Default,,0000,0000,0000,,或者101,000帕斯卡多一點
Dialogue: 0,0:08:41.34,0:08:44.25,Default,,0000,0000,0000,,當然 一帕斯卡是一牛頓每平方米
Dialogue: 0,0:08:44.25,0:08:45.97,Default,,0000,0000,0000,,在所有這些中 單位都是
Dialogue: 0,0:08:45.97,0:08:47.66,Default,,0000,0000,0000,,最難掌握的部分
Dialogue: 0,0:08:47.66,0:08:49.74,Default,,0000,0000,0000,,但假如我們設
Dialogue: 0,0:08:49.74,0:08:50.68,Default,,0000,0000,0000,,這些不同的
Dialogue: 0,0:08:50.68,0:08:52.20,Default,,0000,0000,0000,,標準溫度與壓力
Dialogue: 0,0:08:52.20,0:08:54.88,Default,,0000,0000,0000,,來自於不同的標準設定組織
Dialogue: 0,0:08:54.88,0:08:55.78,Default,,0000,0000,0000,,他們不能完全達成一致
Dialogue: 0,0:08:55.78,0:08:57.26,Default,,0000,0000,0000,,但如果我們把這個當成
Dialogue: 0,0:08:57.26,0:09:00.89,Default,,0000,0000,0000,,標準溫度和壓力的定義
Dialogue: 0,0:09:00.89,0:09:04.60,Default,,0000,0000,0000,,所以我們設溫度
Dialogue: 0,0:09:04.60,0:09:07.23,Default,,0000,0000,0000,,等於0攝氏度
Dialogue: 0,0:09:07.23,0:09:11.20,Default,,0000,0000,0000,,也就等於273開氏度
Dialogue: 0,0:09:11.20,0:09:15.26,Default,,0000,0000,0000,,壓力我們設爲1大氣壓
Dialogue: 0,0:09:15.26,0:09:16.08,Default,,0000,0000,0000,,也可以寫成
Dialogue: 0,0:09:16.08,0:09:22.44,Default,,0000,0000,0000,,101.325或3/8千帕
Dialogue: 0,0:09:22.44,0:09:26.35,Default,,0000,0000,0000,,我的問題是如果我有一種理想氣體
Dialogue: 0,0:09:26.35,0:09:30.02,Default,,0000,0000,0000,,在標準溫度與壓力的情況下
Dialogue: 0,0:09:30.02,0:09:36.45,Default,,0000,0000,0000,,1升中有多少莫耳？
Dialogue: 0,0:09:36.45,0:09:37.58,Default,,0000,0000,0000,,不 我換一種說法
Dialogue: 0,0:09:37.58,0:09:40.87,Default,,0000,0000,0000,,1莫耳會占多少升？
Dialogue: 0,0:09:40.87,0:09:43.78,Default,,0000,0000,0000,,我再多說一點
Dialogue: 0,0:09:43.78,0:09:46.38,Default,,0000,0000,0000,,n等於1莫耳
Dialogue: 0,0:09:46.38,0:09:48.94,Default,,0000,0000,0000,,我想算出體積是什麽
Dialogue: 0,0:09:48.94,0:09:50.66,Default,,0000,0000,0000,,如果我有1莫耳氣體
Dialogue: 0,0:09:50.66,0:09:55.56,Default,,0000,0000,0000,,我有6.02乘10的23次方個這種氣體氣體的分子
Dialogue: 0,0:09:55.56,0:09:58.46,Default,,0000,0000,0000,,在標準壓力1大氣壓
Dialogue: 0,0:09:58.46,0:10:01.00,Default,,0000,0000,0000,,以及標準溫度273度
Dialogue: 0,0:10:01.00,0:10:03.46,Default,,0000,0000,0000,,氣體的體積是多少？
Dialogue: 0,0:10:03.46,0:10:07.74,Default,,0000,0000,0000,,我們應用PV＝nRT
Dialogue: 0,0:10:07.74,0:10:10.10,Default,,0000,0000,0000,,壓力是1大氣壓
Dialogue: 0,0:10:10.10,0:10:11.75,Default,,0000,0000,0000,,但記住我們用的是大氣壓
Dialogue: 0,0:10:11.75,0:10:15.36,Default,,0000,0000,0000,,1大氣壓乘體積
Dialogue: 0,0:10:15.36,0:10:16.66,Default,,0000,0000,0000,,這是我們要解的
Dialogue: 0,0:10:16.66,0:10:18.04,Default,,0000,0000,0000,,我用紫色做
Dialogue: 0,0:10:18.04,0:10:22.01,Default,,0000,0000,0000,,等於1莫耳 我們有1莫耳這種氣體
Dialogue: 0,0:10:22.01,0:10:29.31,Default,,0000,0000,0000,,乘R 乘溫度 乘273
Dialogue: 0,0:10:29.31,0:10:31.79,Default,,0000,0000,0000,,現在這是開氏度 這是莫耳
Dialogue: 0,0:10:31.79,0:10:39.51,Default,,0000,0000,0000,,我們想讓體積是升
Dialogue: 0,0:10:39.51,0:10:41.56,Default,,0000,0000,0000,,所以用哪一個版本的R呢？
Dialogue: 0,0:10:41.56,0:10:44.41,Default,,0000,0000,0000,,我們用的大氣壓
Dialogue: 0,0:10:44.41,0:10:46.61,Default,,0000,0000,0000,,我們想要升的體積
Dialogue: 0,0:10:46.61,0:10:48.03,Default,,0000,0000,0000,,當然 我們有開氏度的莫耳
Dialogue: 0,0:10:48.03,0:10:50.53,Default,,0000,0000,0000,,所以用這個版本 0.082
Dialogue: 0,0:10:50.53,0:10:52.21,Default,,0000,0000,0000,,那麽這是1
Dialogue: 0,0:10:52.21,0:10:54.87,Default,,0000,0000,0000,,我們可以忽略這個1
Dialogue: 0,0:10:54.87,0:10:56.39,Default,,0000,0000,0000,,因此體積等於
Dialogue: 0,0:10:56.39,0:11:02.20,Default,,0000,0000,0000,,0.082乘273開氏度
Dialogue: 0,0:11:02.20,0:11:19.23,Default,,0000,0000,0000,,0.082乘273等於22.4升
Dialogue: 0,0:11:19.23,0:11:21.43,Default,,0000,0000,0000,,所以如果我有任何一種理想氣體
Dialogue: 0,0:11:21.43,0:11:24.08,Default,,0000,0000,0000,,所有的氣體都不是完全理想化的理想
Dialogue: 0,0:11:24.08,0:11:25.48,Default,,0000,0000,0000,,但如果我有一種理想氣體
Dialogue: 0,0:11:25.48,0:11:26.93,Default,,0000,0000,0000,,它在標準溫度
Dialogue: 0,0:11:26.93,0:11:29.10,Default,,0000,0000,0000,,也就是0攝氏度
Dialogue: 0,0:11:29.10,0:11:30.42,Default,,0000,0000,0000,,或者水的熔點
Dialogue: 0,0:11:30.42,0:11:32.42,Default,,0000,0000,0000,,也就是273開氏度
Dialogue: 0,0:11:32.42,0:11:33.71,Default,,0000,0000,0000,,我有一莫耳這種氣體
Dialogue: 0,0:11:33.71,0:11:37.56,Default,,0000,0000,0000,,它在標準壓力 1大氣壓
Dialogue: 0,0:11:37.56,0:11:42.48,Default,,0000,0000,0000,,那個氣體應該占22.4升
Dialogue: 0,0:11:42.48,0:11:44.80,Default,,0000,0000,0000,,如果你想知道多少立方米
Dialogue: 0,0:11:44.80,0:11:46.38,Default,,0000,0000,0000,,它會占
Dialogue: 0,0:11:46.38,0:11:50.99,Default,,0000,0000,0000,,你只用把22.4升乘
Dialogue: 0,0:11:50.99,0:11:53.24,Default,,0000,0000,0000,,現在 這是多少立方米
Dialogue: 0,0:11:53.24,0:11:57.50,Default,,0000,0000,0000,,對於每一立方米都有1000升
Dialogue: 0,0:11:57.50,0:11:59.63,Default,,0000,0000,0000,,我知道這看起來很多 但這是真的
Dialogue: 0,0:11:59.63,0:12:02.48,Default,,0000,0000,0000,,只要想想一立方米有多大
Dialogue: 0,0:12:02.48,0:12:09.36,Default,,0000,0000,0000,,所以這就是0.0224立方米
Dialogue: 0,0:12:09.36,0:12:12.45,Default,,0000,0000,0000,,如果你有1大氣壓的某種東西 一莫耳
Dialogue: 0,0:12:12.45,0:12:14.75,Default,,0000,0000,0000,,在0攝氏度情況下
Dialogue: 0,0:12:14.75,0:12:16.08,Default,,0000,0000,0000,,反正這其實是
Dialogue: 0,0:12:16.08,0:12:17.71,Default,,0000,0000,0000,,很有用的數字
Dialogue: 0,0:12:17.71,0:12:22.25,Default,,0000,0000,0000,,人們會經常說你有2莫耳
Dialogue: 0,0:12:22.25,0:12:25.29,Default,,0000,0000,0000,,在標準溫度與氣壓
Dialogue: 0,0:12:25.29,0:12:26.97,Default,,0000,0000,0000,,它會占多少升？
Dialogue: 0,0:12:26.97,0:12:29.61,Default,,0000,0000,0000,,好的 1莫耳占這麽多
Dialogue: 0,0:12:29.61,0:12:31.78,Default,,0000,0000,0000,,2莫耳在標準溫度與氣壓
Dialogue: 0,0:12:31.78,0:12:33.44,Default,,0000,0000,0000,,就會占兩倍體積
Dialogue: 0,0:12:33.44,0:12:34.80,Default,,0000,0000,0000,,因爲你只是用PV＝nRT
Dialogue: 0,0:12:34.80,0:12:36.27,Default,,0000,0000,0000,,然後加倍
Dialogue: 0,0:12:36.27,0:12:38.79,Default,,0000,0000,0000,,其他都不變
Dialogue: 0,0:12:38.79,0:12:40.99,Default,,0000,0000,0000,,壓力 其他一切都是固定的
Dialogue: 0,0:12:40.99,0:12:43.04,Default,,0000,0000,0000,,所以如果你把莫耳數加倍
Dialogue: 0,0:12:43.04,0:12:44.21,Default,,0000,0000,0000,,就會把體積加倍
Dialogue: 0,0:12:44.21,0:12:46.11,Default,,0000,0000,0000,,或者如果你把莫耳數減半
Dialogue: 0,0:12:46.11,0:12:47.67,Default,,0000,0000,0000,,就會把它的體積減半
Dialogue: 0,0:12:47.67,0:12:49.66,Default,,0000,0000,0000,,所以一個很有用的知識點是在升的單位中
Dialogue: 0,0:12:49.66,0:12:52.02,Default,,0000,0000,0000,,以及標準溫度與氣壓的情況下
Dialogue: 0,0:12:52.02,0:12:52.91,Default,,0000,0000,0000,,當標準溫度與氣壓
Dialogue: 0,0:12:52.91,0:12:56.52,Default,,0000,0000,0000,,被定義爲1大氣壓以及273開氏度
Dialogue: 0,0:12:56.52,0:13:00.16,Default,,0000,0000,0000,,一種理想氣體會占22.4升的體積