[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,,我们来多做点题吧
Dialogue: 0,0:00:02.14,0:00:04.56,Default,,0000,0000,0000,,关于理想气体状态方程的题目
Dialogue: 0,0:00:04.56,0:00:06.68,Default,,0000,0000,0000,,假设我有一罐气体
Dialogue: 0,0:00:06.68,0:00:15.32,Default,,0000,0000,0000,,当前压强是3个大气压
Dialogue: 0,0:00:15.32,0:00:19.76,Default,,0000,0000,0000,,假设罐子的体积是
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,,现在 气压会如何改变
Dialogue: 0,0:00:30.14,0:00:39.28,Default,,0000,0000,0000,,如果体积从9升变为3升
Dialogue: 0,0:00:39.28,0:00:42.18,Default,,0000,0000,0000,,从第一个理想气体状态方程的视频中
Dialogue: 0,0:00:42.18,0:00:43.35,Default,,0000,0000,0000,,你可以大概感觉到
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,,这很重要
Dialogue: 0,0:00:47.90,0:00:50.76,Default,,0000,0000,0000,,我们保持温度不变
Dialogue: 0,0:00:50.76,0:00:52.54,Default,,0000,0000,0000,,这很重要 必须明白
Dialogue: 0,0:00:52.54,0:00:58.38,Default,,0000,0000,0000,,所以在我们的直觉
Dialogue: 0,0:00:58.38,0:01:00.35,Default,,0000,0000,0000,,在理想气体状态方程背后 我们说
Dialogue: 0,0:01:00.35,0:01:02.99,Default,,0000,0000,0000,,看 如果我们有一定量的粒子
Dialogue: 0,0:01:02.99,0:01:06.85,Default,,0000,0000,0000,,以及一定的动能
Dialogue: 0,0:01:06.85,0:01:08.83,Default,,0000,0000,0000,,他们施加一定的压力
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,,如果我们要让容器变小
Dialogue: 0,0:01:14.37,0:01:16.20,Default,,0000,0000,0000,,我们有同样数量的粒子
Dialogue: 0,0:01:16.20,0:01:17.43,Default,,0000,0000,0000,,n不变
Dialogue: 0,0:01:17.43,0:01:19.88,Default,,0000,0000,0000,,平均动能不变
Dialogue: 0,0:01:19.88,0:01:21.66,Default,,0000,0000,0000,,所以它们会更频繁地撞上容器壁
Dialogue: 0,0:01:21.66,0:01:24.22,Default,,0000,0000,0000,,所以当我们使容器缩小时
Dialogue: 0,0:01:24.22,0:01:26.73,Default,,0000,0000,0000,,当体积变大
Dialogue: 0,0:01:26.73,0:01:27.76,Default,,0000,0000,0000,,当体积变小时
Dialogue: 0,0:01:27.76,0:01:30.07,Default,,0000,0000,0000,,气压应该升高
Dialogue: 0,0:01:30.07,0:01:32.62,Default,,0000,0000,0000,,所以我们看看能不能算出准确数字
Dialogue: 0,0:01:32.62,0:01:35.43,Default,,0000,0000,0000,,我们可以用理想气体方程了
Dialogue: 0,0:01:35.43,0:01:41.87,Default,,0000,0000,0000,,压强乘体积等于nRT
Dialogue: 0,0:01:41.87,0:01:44.32,Default,,0000,0000,0000,,现在 粒子数改变了吗
Dialogue: 0,0:01:44.32,0:01:47.98,Default,,0000,0000,0000,,在我改变情况缩小了体积时？
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,,我们有一样的粒子数
Dialogue: 0,0:01:49.76,0:01:50.92,Default,,0000,0000,0000,,我只是把容器缩小了
Dialogue: 0,0:01:50.92,0:01:55.20,Default,,0000,0000,0000,,所以n还是n R不变 那是个常数
Dialogue: 0,0:01:55.20,0:01:57.22,Default,,0000,0000,0000,,温度不变
Dialogue: 0,0:01:57.22,0:02:00.32,Default,,0000,0000,0000,,所以我原先的压强乘体积
Dialogue: 0,0:02:00.32,0:02:02.69,Default,,0000,0000,0000,,等于nRT
Dialogue: 0,0:02:02.69,0:02:04.31,Default,,0000,0000,0000,,而我的新压强乘体积——
Dialogue: 0,0:02:04.31,0:02:07.95,Default,,0000,0000,0000,,让我叫这个P1和V1
Dialogue: 0,0:02:07.95,0:02:11.00,Default,,0000,0000,0000,,然后P2是这个
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是这个 我们要算出P2
Dialogue: 0,0:02:21.70,0:02:23.13,Default,,0000,0000,0000,,P2是什么？
Dialogue: 0,0:02:23.13,0:02:31.35,Default,,0000,0000,0000,,我们知道P1乘V1等于nRT
Dialogue: 0,0:02:31.35,0:02:33.40,Default,,0000,0000,0000,,我们还知道既然气体的温度和
Dialogue: 0,0:02:33.40,0:02:35.98,Default,,0000,0000,0000,,摩尔数都不变
Dialogue: 0,0:02:35.98,0:02:40.79,Default,,0000,0000,0000,,P2乘V2等于nRT
Dialogue: 0,0:02:40.79,0:02:43.20,Default,,0000,0000,0000,,既然它们都等于同一个东西
Dialogue: 0,0:02:43.20,0:02:45.67,Default,,0000,0000,0000,,我们可以说压强乘体积
Dialogue: 0,0:02:45.67,0:02:47.80,Default,,0000,0000,0000,,只要温度不变
Dialogue: 0,0:02:47.80,0:02:49.20,Default,,0000,0000,0000,,就也不变
Dialogue: 0,0:02:49.20,0:02:55.76,Default,,0000,0000,0000,,所以P1乘V1也等于P2乘V2
Dialogue: 0,0:02:55.76,0:02:57.94,Default,,0000,0000,0000,,那P1是什么？
Dialogue: 0,0:02:57.94,0:03:03.23,Default,,0000,0000,0000,,P1 我们原先的压强 是3个大气压
Dialogue: 0,0:03:06.63,0:03:12.02,Default,,0000,0000,0000,,所以3大气压乘9升等于
Dialogue: 0,0:03:12.02,0:03:15.98,Default,,0000,0000,0000,,我们的新气压乘3升
Dialogue: 0,0:03:15.98,0:03:18.99,Default,,0000,0000,0000,,如果我们将等式两边同除以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,,我们还有9大气压
Dialogue: 0,0:03:33.64,0:03:34.80,Default,,0000,0000,0000,,这有道理
Dialogue: 0,0:03:34.80,0:03:39.26,Default,,0000,0000,0000,,当你把体积缩小2/3
Dialogue: 0,0:03:39.26,0:03:40.30,Default,,0000,0000,0000,,或者当你使体积
Dialogue: 0,0:03:40.30,0:03:42.94,Default,,0000,0000,0000,,变为原来的1/3
Dialogue: 0,0:03:42.94,0:03:46.20,Default,,0000,0000,0000,,你的压强就会增加3倍
Dialogue: 0,0:03:46.20,0:03:51.57,Default,,0000,0000,0000,,所以这个乘3 这个乘1/3
Dialogue: 0,0:03:51.57,0:03:52.90,Default,,0000,0000,0000,,一般这是很有用的知识
Dialogue: 0,0:03:52.90,0:03:55.20,Default,,0000,0000,0000,,如果温度不变
Dialogue: 0,0:03:55.20,0:03:57.48,Default,,0000,0000,0000,,那么压强乘体积
Dialogue: 0,0:03:57.48,0:03:59.11,Default,,0000,0000,0000,,也是一个常数
Dialogue: 0,0:03:59.11,0:04:00.96,Default,,0000,0000,0000,,现在 你可以更进一步
Dialogue: 0,0:04:00.96,0:04:06.88,Default,,0000,0000,0000,,如果我们看看PV＝nRT
Dialogue: 0,0:04:06.88,0:04:09.16,Default,,0000,0000,0000,,我们知道两个量不变
Dialogue: 0,0:04:09.16,0:04:11.84,Default,,0000,0000,0000,,在我们做的大部分练习中
Dialogue: 0,0:04:11.84,0:04:13.54,Default,,0000,0000,0000,,就是分子数
Dialogue: 0,0:04:13.54,0:04:15.53,Default,,0000,0000,0000,,以及显然R不会变
Dialogue: 0,0:04:15.53,0:04:18.26,Default,,0000,0000,0000,,所以如果我们将两边同除以T
Dialogue: 0,0:04:18.26,0:04:23.16,Default,,0000,0000,0000,,我们就有了PV/T＝nR
Dialogue: 0,0:04:23.16,0:04:24.92,Default,,0000,0000,0000,,或者可以说它等于一个常数
Dialogue: 0,0:04:24.92,0:04:27.20,Default,,0000,0000,0000,,它对于任何系统都是一个常数
Dialogue: 0,0:04:27.20,0:04:28.63,Default,,0000,0000,0000,,如果我们不改变
Dialogue: 0,0:04:28.63,0:04:31.52,Default,,0000,0000,0000,,容器中的分子数的话
Dialogue: 0,0:04:31.52,0:04:33.37,Default,,0000,0000,0000,,所以 如果我们改变压强——
Dialogue: 0,0:04:33.37,0:04:35.65,Default,,0000,0000,0000,,如果一开始有
Dialogue: 0,0:04:35.65,0:04:40.00,Default,,0000,0000,0000,,压强1 体积1 以及某个温度1
Dialogue: 0,0:04:40.00,0:04:41.50,Default,,0000,0000,0000,,那就等于这个常数
Dialogue: 0,0:04:41.50,0:04:44.19,Default,,0000,0000,0000,,如果我们改变其中一个
Dialogue: 0,0:04:44.19,0:04:44.73,Default,,0000,0000,0000,,我们回到
Dialogue: 0,0:04:44.73,0:04:48.86,Default,,0000,0000,0000,,压强2 体积2 温度2
Dialogue: 0,0:04:48.86,0:04:50.47,Default,,0000,0000,0000,,他们应该还等于这个常数
Dialogue: 0,0:04:50.47,0:04:51.47,Default,,0000,0000,0000,,所以他们相等
Dialogue: 0,0:04:51.47,0:04:55.35,Default,,0000,0000,0000,,举例来说 假设我开始有
Dialogue: 0,0:04:55.35,0:05:01.08,Default,,0000,0000,0000,,1个大气压的压强
Dialogue: 0,0:05:01.08,0:05:05.07,Default,,0000,0000,0000,,而体积是——
Dialogue: 0,0:05:05.07,0:05:08.61,Default,,0000,0000,0000,,我换一下单位来试一种不同的做法
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,,假设温度是27摄氏度
Dialogue: 0,0:05:20.21,0:05:21.74,Default,,0000,0000,0000,,我刚写了摄氏度
Dialogue: 0,0:05:21.74,0:05:22.70,Default,,0000,0000,0000,,以为我想让你永远记住
Dialogue: 0,0:05:22.70,0:05:23.97,Default,,0000,0000,0000,,你要转换成开氏度
Dialogue: 0,0:05:23.97,0:05:27.83,Default,,0000,0000,0000,,所以27摄氏度加上273是
Dialogue: 0,0:05:27.83,0:05:33.15,Default,,0000,0000,0000,,正好300开氏度
Dialogue: 0,0:05:33.15,0:05:39.53,Default,,0000,0000,0000,,我们的新温度是
Dialogue: 0,0:05:39.53,0:05:40.63,Default,,0000,0000,0000,,实际上我们来算一下新温度
Dialogue: 0,0:05:40.63,0:05:41.42,Default,,0000,0000,0000,,会是什么
Dialogue: 0,0:05:41.42,0:05:46.27,Default,,0000,0000,0000,,假设新压强是2大气压
Dialogue: 0,0:05:46.27,0:05:47.88,Default,,0000,0000,0000,,压强增加了
Dialogue: 0,0:05:47.88,0:05:50.01,Default,,0000,0000,0000,,我们让容器缩小
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,,所以容器缩小了一半
Dialogue: 0,0:05:55.10,0:05:56.68,Default,,0000,0000,0000,,而压强增加了一半
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,,你知道我们让压强升高了
Dialogue: 0,0:06:02.15,0:06:08.18,Default,,0000,0000,0000,,我来让容器更小一点
Dialogue: 0,0:06:08.18,0:06:08.77,Default,,0000,0000,0000,,实际上 算了
Dialogue: 0,0:06:08.77,0:06:10.71,Default,,0000,0000,0000,,我来让压强更大
Dialogue: 0,0:06:10.71,0:06:14.26,Default,,0000,0000,0000,,让压强变成5个大气压
Dialogue: 0,0:06:14.26,0:06:16.94,Default,,0000,0000,0000,,现在我们想知道第二个温度是什么
Dialogue: 0,0:06:16.94,0:06:18.81,Default,,0000,0000,0000,,我们建立起等式
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大气压乘立方米每开氏度
Dialogue: 0,0:06:28.10,0:06:32.69,Default,,0000,0000,0000,,等于2/T2 我们的新温度
Dialogue: 0,0:06:32.69,0:06:40.15,Default,,0000,0000,0000,,然后我们有1500等于2T2
Dialogue: 0,0:06:40.15,0:06:41.37,Default,,0000,0000,0000,,两边同除以2
Dialogue: 0,0:06:41.37,0:06:46.90,Default,,0000,0000,0000,,得到了T2等于750开氏度
Dialogue: 0,0:06:46.90,0:06:48.31,Default,,0000,0000,0000,,这有道理 对吧
Dialogue: 0,0:06:48.31,0:06:50.54,Default,,0000,0000,0000,,我们让压强升高了这么多
Dialogue: 0,0:06:50.54,0:06:53.29,Default,,0000,0000,0000,,而同时也减小了体积
Dialogue: 0,0:06:53.29,0:06:55.64,Default,,0000,0000,0000,,所以温度必须上升
Dialogue: 0,0:06:55.64,0:06:56.55,Default,,0000,0000,0000,,或者如果这么想
Dialogue: 0,0:06:56.55,0:06:58.18,Default,,0000,0000,0000,,或许我们升高了温度
Dialogue: 0,0:06:58.18,0:06:59.50,Default,,0000,0000,0000,,因此也使压强
Dialogue: 0,0:06:59.50,0:07:00.69,Default,,0000,0000,0000,,变得高多了
Dialogue: 0,0:07:00.69,0:07:03.87,Default,,0000,0000,0000,,尤其是当我们减小了体积时
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,,压强升高了这么多
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,,他从1大气压变为5大气压
Dialogue: 0,0:07:12.48,0:07:14.37,Default,,0000,0000,0000,,因为一面
Dialogue: 0,0:07:14.37,0:07:18.03,Default,,0000,0000,0000,,我们将体积缩小了1/2
Dialogue: 0,0:07:18.03,0:07:19.68,Default,,0000,0000,0000,,所以压强应该加倍了
Dialogue: 0,0:07:19.68,0:07:21.90,Default,,0000,0000,0000,,我们就到了2大气压
Dialogue: 0,0:07:21.90,0:07:23.78,Default,,0000,0000,0000,,然后我们让温度高多了
Dialogue: 0,0:07:23.78,0:07:25.41,Default,,0000,0000,0000,,所以我们也在撞上容器壁
Dialogue: 0,0:07:25.41,0:07:27.90,Default,,0000,0000,0000,,我们使温度变为750开氏度
Dialogue: 0,0:07:27.90,0:07:29.89,Default,,0000,0000,0000,,所以温度升高了两倍还多
Dialogue: 0,0:07:29.89,0:07:33.88,Default,,0000,0000,0000,,于是我们得到了5大气压
Dialogue: 0,0:07:33.88,0:07:37.99,Default,,0000,0000,0000,,现在 另一件你可能会听到的概念
Dialogue: 0,0:07:37.99,0:07:39.69,Default,,0000,0000,0000,,是发生什么
Dialogue: 0,0:07:39.69,0:07:42.48,Default,,0000,0000,0000,,在标准温度和气压下
Dialogue: 0,0:07:42.48,0:07:44.04,Default,,0000,0000,0000,,我把这些都删了
Dialogue: 0,0:07:44.04,0:07:47.57,Default,,0000,0000,0000,,标准温度和气压
Dialogue: 0,0:07:47.57,0:07:51.53,Default,,0000,0000,0000,,我把这些不需要的都删掉
Dialogue: 0,0:07:52.89,0:07:56.81,Default,,0000,0000,0000,,标准温度和气压
Dialogue: 0,0:07:56.81,0:07:57.47,Default,,0000,0000,0000,,我提到这个
Dialogue: 0,0:07:57.47,0:07:58.69,Default,,0000,0000,0000,,是因为虽然它被称作
Dialogue: 0,0:07:58.69,0:07:59.88,Default,,0000,0000,0000,,标准温度和气压
Dialogue: 0,0:07:59.88,0:08:03.70,Default,,0000,0000,0000,,有时也称作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,,人们还没有完全标准化
Dialogue: 0,0:08:07.84,0:08:13.74,Default,,0000,0000,0000,,标准气压和温度是什么
Dialogue: 0,0:08:13.74,0:08:15.92,Default,,0000,0000,0000,,我在维基百科上查了一下
Dialogue: 0,0:08:15.92,0:08:16.88,Default,,0000,0000,0000,,你可能会看到的
Dialogue: 0,0:08:16.88,0:08:19.99,Default,,0000,0000,0000,,在大部分物理课以及标准化考试上的
Dialogue: 0,0:08:19.99,0:08:23.94,Default,,0000,0000,0000,,标准温度是0摄氏度
Dialogue: 0,0:08:23.94,0:08:26.84,Default,,0000,0000,0000,,也就是 当然 273开氏度
Dialogue: 0,0:08:26.84,0:08:30.30,Default,,0000,0000,0000,,标准气压是1个大气压
Dialogue: 0,0:08:30.30,0:08:31.24,Default,,0000,0000,0000,,在维基百科上
Dialogue: 0,0:08:31.24,0:08:38.53,Default,,0000,0000,0000,,他们写成101.325千帕斯卡
Dialogue: 0,0:08:38.53,0:08:41.34,Default,,0000,0000,0000,,或者101,000帕斯卡多一点
Dialogue: 0,0:08:41.34,0:08:44.25,Default,,0000,0000,0000,,当然 一帕斯卡是一牛顿每平方米
Dialogue: 0,0:08:44.25,0:08:45.97,Default,,0000,0000,0000,,在所有这些中 单位都是
Dialogue: 0,0:08:45.97,0:08:47.66,Default,,0000,0000,0000,,最难掌握的部分
Dialogue: 0,0:08:47.66,0:08:49.74,Default,,0000,0000,0000,,但假如我们设
Dialogue: 0,0:08:49.74,0:08:50.68,Default,,0000,0000,0000,,这些不同的
Dialogue: 0,0:08:50.68,0:08:52.20,Default,,0000,0000,0000,,标准温度与压强
Dialogue: 0,0:08:52.20,0:08:54.88,Default,,0000,0000,0000,,来自于不同的标准设定组织
Dialogue: 0,0:08:54.88,0:08:55.78,Default,,0000,0000,0000,,他们不能完全达成一致
Dialogue: 0,0:08:55.78,0:08:57.26,Default,,0000,0000,0000,,但如果我们把这个当成
Dialogue: 0,0:08:57.26,0:09:00.89,Default,,0000,0000,0000,,标准温度和压强的定义
Dialogue: 0,0:09:00.89,0:09:04.60,Default,,0000,0000,0000,,所以我们设温度
Dialogue: 0,0:09:04.60,0:09:07.23,Default,,0000,0000,0000,,等于0摄氏度
Dialogue: 0,0:09:07.23,0:09:11.20,Default,,0000,0000,0000,,也就等于273开氏度
Dialogue: 0,0:09:11.20,0:09:15.26,Default,,0000,0000,0000,,压强我们设为1大气压
Dialogue: 0,0:09:15.26,0:09:16.08,Default,,0000,0000,0000,,也可以写成
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,,我的问题是如果我有一种理想气体
Dialogue: 0,0:09:26.35,0:09:30.02,Default,,0000,0000,0000,,在标准温度与压强的情况下
Dialogue: 0,0:09:30.02,0:09:36.45,Default,,0000,0000,0000,,1升中有多少摩尔？
Dialogue: 0,0:09:36.45,0:09:37.58,Default,,0000,0000,0000,,不 我换一种说法
Dialogue: 0,0:09:37.58,0:09:40.87,Default,,0000,0000,0000,,1摩尔会占多少升？
Dialogue: 0,0:09:40.87,0:09:43.78,Default,,0000,0000,0000,,我再多说一点
Dialogue: 0,0:09:43.78,0:09:46.38,Default,,0000,0000,0000,,n等于1摩尔
Dialogue: 0,0:09:46.38,0:09:48.94,Default,,0000,0000,0000,,我想算出体积是什么
Dialogue: 0,0:09:48.94,0:09:50.66,Default,,0000,0000,0000,,如果我有1摩尔气体
Dialogue: 0,0:09:50.66,0:09:55.56,Default,,0000,0000,0000,,我有6.02乘10的23次方个这种气体气体的分子
Dialogue: 0,0:09:55.56,0:09:58.46,Default,,0000,0000,0000,,在标准压强1大气压
Dialogue: 0,0:09:58.46,0:10:01.00,Default,,0000,0000,0000,,以及标准温度273度
Dialogue: 0,0:10:01.00,0:10:03.46,Default,,0000,0000,0000,,气体的体积是多少？
Dialogue: 0,0:10:03.46,0:10:07.74,Default,,0000,0000,0000,,我们应用PV＝nRT
Dialogue: 0,0:10:07.74,0:10:10.10,Default,,0000,0000,0000,,压强是1大气压
Dialogue: 0,0:10:10.10,0:10:11.75,Default,,0000,0000,0000,,但记住我们用的是大气压
Dialogue: 0,0:10:11.75,0:10:15.36,Default,,0000,0000,0000,,1大气压乘体积
Dialogue: 0,0:10:15.36,0:10:16.66,Default,,0000,0000,0000,,这是我们要解的
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,,等于1摩尔 我们有1摩尔这种气体
Dialogue: 0,0:10:22.01,0:10:29.31,Default,,0000,0000,0000,,乘R 乘温度 乘273
Dialogue: 0,0:10:29.31,0:10:31.79,Default,,0000,0000,0000,,现在这是开氏度 这是摩尔
Dialogue: 0,0:10:31.79,0:10:39.51,Default,,0000,0000,0000,,我们想让体积是升
Dialogue: 0,0:10:39.51,0:10:41.56,Default,,0000,0000,0000,,所以用哪一个版本的R呢？
Dialogue: 0,0:10:41.56,0:10:44.41,Default,,0000,0000,0000,,我们用的大气压
Dialogue: 0,0:10:44.41,0:10:46.61,Default,,0000,0000,0000,,我们想要升的体积
Dialogue: 0,0:10:46.61,0:10:48.03,Default,,0000,0000,0000,,当然 我们有开氏度的摩尔
Dialogue: 0,0:10:48.03,0:10:50.53,Default,,0000,0000,0000,,所以用这个版本 0.082
Dialogue: 0,0:10:50.53,0:10:52.21,Default,,0000,0000,0000,,那么这是1
Dialogue: 0,0:10:52.21,0:10:54.87,Default,,0000,0000,0000,,我们可以忽略这个1
Dialogue: 0,0:10:54.87,0:10:56.39,Default,,0000,0000,0000,,因此体积等于
Dialogue: 0,0:10:56.39,0:11:02.20,Default,,0000,0000,0000,,0.082乘273开氏度
Dialogue: 0,0:11:02.20,0:11:19.23,Default,,0000,0000,0000,,0.082乘273等于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种理想气体
Dialogue: 0,0:11:21.43,0:11:24.08,Default,,0000,0000,0000,,所有的气体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,,但如果我有一种理想气体
Dialogue: 0,0:11:25.48,0:11:26.93,Default,,0000,0000,0000,,它在标准温度
Dialogue: 0,0:11:26.93,0:11:29.10,Default,,0000,0000,0000,,也就是0摄氏度
Dialogue: 0,0:11:29.10,0:11:30.42,Default,,0000,0000,0000,,或者水的熔点
Dialogue: 0,0:11:30.42,0:11:32.42,Default,,0000,0000,0000,,也就是273开氏度
Dialogue: 0,0:11:32.42,0:11:33.71,Default,,0000,0000,0000,,我有一摩尔这种气体
Dialogue: 0,0:11:33.71,0:11:37.56,Default,,0000,0000,0000,,它在标准压强 1大气压
Dialogue: 0,0:11:37.56,0:11:42.48,Default,,0000,0000,0000,,那个气体应该占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,,它会占
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,,现在 这是多少立方米
Dialogue: 0,0:11:53.24,0:11:57.50,Default,,0000,0000,0000,,对于每一立方米都有1000升
Dialogue: 0,0:11:57.50,0:11:59.63,Default,,0000,0000,0000,,我知道这看起来很多 但这是真的
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,,所以这就是0.0224立方米
Dialogue: 0,0:12:09.36,0:12:12.45,Default,,0000,0000,0000,,如果你有1大气压的某种东西 一摩尔
Dialogue: 0,0:12:12.45,0:12:14.75,Default,,0000,0000,0000,,在0摄氏度情况下
Dialogue: 0,0:12:14.75,0:12:16.08,Default,,0000,0000,0000,,反正这其实是
Dialogue: 0,0:12:16.08,0:12:17.71,Default,,0000,0000,0000,,很有用的数字
Dialogue: 0,0:12:17.71,0:12:22.25,Default,,0000,0000,0000,,人们会经常说你有2摩尔
Dialogue: 0,0:12:22.25,0:12:25.29,Default,,0000,0000,0000,,在标准温度与气压
Dialogue: 0,0:12:25.29,0:12:26.97,Default,,0000,0000,0000,,它会占多少升？
Dialogue: 0,0:12:26.97,0:12:29.61,Default,,0000,0000,0000,,好的 1摩尔占这么多
Dialogue: 0,0:12:29.61,0:12:31.78,Default,,0000,0000,0000,,2摩尔在标准温度与气压
Dialogue: 0,0:12:31.78,0:12:33.44,Default,,0000,0000,0000,,就会占两倍体积
Dialogue: 0,0:12:33.44,0:12:34.80,Default,,0000,0000,0000,,因为你只是用PV＝nRT
Dialogue: 0,0:12:34.80,0:12:36.27,Default,,0000,0000,0000,,然后加倍
Dialogue: 0,0:12:36.27,0:12:38.79,Default,,0000,0000,0000,,其他都不变
Dialogue: 0,0:12:38.79,0:12:40.99,Default,,0000,0000,0000,,压强 其他一切都是固定的
Dialogue: 0,0:12:40.99,0:12:43.04,Default,,0000,0000,0000,,所以如果你把摩尔数加倍
Dialogue: 0,0:12:43.04,0:12:44.21,Default,,0000,0000,0000,,就会把体积加倍
Dialogue: 0,0:12:44.21,0:12:46.11,Default,,0000,0000,0000,,或者如果你把摩尔数减半
Dialogue: 0,0:12:46.11,0:12:47.67,Default,,0000,0000,0000,,就会把它的体积减半
Dialogue: 0,0:12:47.67,0:12:49.66,Default,,0000,0000,0000,,所以一个很有用的知识点是在升的单位中
Dialogue: 0,0:12:49.66,0:12:52.02,Default,,0000,0000,0000,,以及标准温度与气压的情况下
Dialogue: 0,0:12:52.02,0:12:52.91,Default,,0000,0000,0000,,当标准温度与气压
Dialogue: 0,0:12:52.91,0:12:56.52,Default,,0000,0000,0000,,被定义为1大气压以及273开氏度
Dialogue: 0,0:12:56.52,0:13:00.16,Default,,0000,0000,0000,,一种理想气体会占22.4升的体积