题目内容
一根两端开口、横截面积为S=2cm2足够长的玻璃管竖直插入水银槽中并固定(插入水银槽中的部分足够深)。管中有一个质量不计的光滑活塞,活塞下封闭着长L=21cm的气柱,气体的温度T1=280K,外界大气压取P0=1.0×105Pa(相当于75cm汞柱高的压强)。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324365882840.png)
①对气体加热,使其温度升高到T2=320K,求此时气柱的长度;
②在活塞上施加一个竖直向上的拉力F=4N,保持气体的温度T2不变,求平衡后气柱的长度及此时管内外水银面的高度差。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324365882840.png)
①对气体加热,使其温度升高到T2=320K,求此时气柱的长度;
②在活塞上施加一个竖直向上的拉力F=4N,保持气体的温度T2不变,求平衡后气柱的长度及此时管内外水银面的高度差。
①
②![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436666647.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324366351373.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436666647.png)
①被封闭气体的
初状态为
,
, ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436775642.png)
末状态为
,
,
根据盖·吕萨克定律,有
,即
①
得
②
②在活塞上施加拉力F后,气体的状态变为
③
根据玻意耳定律,有
,即
④
得
⑤
⑥
所以管内外水银面的高度差为
。 ⑦
初状态为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324367131103.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436744687.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436775642.png)
末状态为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324368381114.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436869557.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436900644.png)
根据盖·吕萨克定律,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436947653.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436978618.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324366351373.png)
②在活塞上施加拉力F后,气体的状态变为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324370562129.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132437119565.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132437181722.png)
根据玻意耳定律,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132437212594.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132437275578.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324373371356.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241324373991351.png)
所以管内外水银面的高度差为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132436666647.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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