题目内容
如图所示,一竖直放置的、长为L的细管下端封闭,上端与大气(视为理想气体)相通,初始时管内气体温度为
。现用一段水银柱从管口开始注入管内将气柱封闭,该过程中气体温度保持不变且没有气体漏出,平衡后管内上下两部分气柱长度比为l∶3。若将管内下部气体温度降至
,在保持温度不变的条件下将管倒置,平衡后水银柱下端与管下端刚好平齐(没有水银漏出)。已知
,大气压强为
,重力加速度为g。求水银柱的长度h和水银的密度
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021127573357.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112679321.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112695363.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112710588.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112726372.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112741312.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021127573357.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112773611.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112804875.png)
试题分析: 设管内截面面积为S,初始时气体压强为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112819366.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112835541.png)
注入水银后下部气体压强为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112866705.png)
体积为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112897856.png)
由玻意耳定律有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021129131240.png)
将管倒置后,管内气体压强为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112944706.png)
体积为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112960707.png)
由理想气体状态方程有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021129751263.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112773611.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112804875.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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