题目内容
如图所示,两个可导热的气缸竖直放置,它们的底部由一细管连通(忽略细管的容积)。两气缸各有一活塞,质量分别为
和
,活塞与气缸壁无摩擦。活塞的下方为理想气体,上方为真空。当气体处于平衡状态时,两活塞位于同一高度h。(已知
=3m,
=2m)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220588255395.jpg)
(1)在两活塞上同时各放一质量为m的物块,求气体再次达到平衡后两活塞的高度差(假定环境的温度始终保持为
)。
(2)在达到上一问的终态后,环境温度由
缓慢上升到T,试问在这个过程中,气体对活塞做了多少功?气体是吸收还是放出了热量?(假定在气体状态变化过程中,两物块均不会碰到气缸顶部)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058684219.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058700325.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058684219.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058700325.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220588255395.jpg)
(1)在两活塞上同时各放一质量为m的物块,求气体再次达到平衡后两活塞的高度差(假定环境的温度始终保持为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058840213.gif)
(2)在达到上一问的终态后,环境温度由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058840213.gif)
⑴两活塞的高度差为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058887374.gif)
⑵![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220589341097.gif)
在此过程中气体吸收热量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058887374.gif)
⑵
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220589341097.gif)
在此过程中气体吸收热量
⑴设左、右活塞的面积分别为A/和A,由于气体处于平衡状态,故两活塞对气体的压强相等,即: ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058949574.gif)
由此得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058981436.gif)
在两个活塞上各加一质量为m的物块后,右活塞降至气缸底部,所有气体都在左气缸中。
在初态,气体的压强为
,体积为
;在末态,气体压强为
,体积为
(x为左活塞的高度)。由玻意耳-马略特定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059059747.gif)
解得:
即两活塞的高度差为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058887374.gif)
⑵当温度由T0上升至T时,气体的压强始终为
,设x/是温度达到T时左活塞的高度,由盖·吕萨克定律得: ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059121613.gif)
活塞对气体做的功为:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220589341097.gif)
在此过程中气体吸收热量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058949574.gif)
由此得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058981436.gif)
在两个活塞上各加一质量为m的物块后,右活塞降至气缸底部,所有气体都在左气缸中。
在初态,气体的压强为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058996419.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059012414.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059027456.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059043399.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059059747.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059074423.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122058887374.gif)
⑵当温度由T0上升至T时,气体的压强始终为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059027456.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122059121613.gif)
活塞对气体做的功为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241220589341097.gif)
在此过程中气体吸收热量
![](http://thumb2018.1010pic.com/images/loading.gif)
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