题目内容
如图所示,两个侧壁绝热、顶部和底部都导热的相同气缸直立放置,气缸底部和顶部均有细管连通,顶部的细管带有阀门K.两气缸的容积均为V0,气缸中各有一个绝热活塞(质量不同,厚度可忽略).开始时K关闭,两活塞下方和右活塞上方充有气体(可视为理想气体),压强分别为
和
;左活塞在气缸正中间,其上方为真空; 右活塞上方气体体积为
.现使气缸底与一恒温热源接触,平衡后左活塞升至气缸顶部,且与顶部刚好没有接触;然后打开K,经过一段时间,重新达到平衡.已知外界温度为
,不计活塞与气缸壁间的摩擦.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242251055384318.jpg)
求:(1)恒温热源的温度T;
(2)重新达到平衡后左气缸中活塞上方气体的体积
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225100343345.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225101669444.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225102543453.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225104118358.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242251055384318.jpg)
求:(1)恒温热源的温度T;
(2)重新达到平衡后左气缸中活塞上方气体的体积
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225105959370.png)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225108674502.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225107332564.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225108674502.png)
试题分析:(1)与恒温热源接触后,在K未打开时,右活塞不动,两活塞下方对气体经历等压过程,由盖·吕萨克定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225110093859.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225107332564.png)
(2)由初始状态的力学平衡条件可知,左活塞的质量比右活塞的大,打开K后,左活塞下降至某一位置,右活塞必须升至气缸顶,才能满足力学平衡条件。
气缸顶部与外界接触,底部与恒温热源接触,两部分气体各自经历等温过程,设左活塞上方气体压强为P,由玻意耳定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225112542768.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242251139151131.png)
联立以上两式解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225114368763.png)
其解为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225115350617.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225115959627.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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