题目内容
如图所示,两气缸AB粗细均匀,等高且内壁光滑,其下部由体积可忽略的细管连通;A的直径为B的2倍,A上端封闭,B上端与大气连通;两气缸除A顶部导热外,其余部分均绝热。两气缸中各有一厚度可忽略的绝热轻活塞a、b,活塞下方充有氮气,活塞a上方充有氧气;当大气压为p0,外界和气缸内气体温度均为7℃且平衡时,活塞a离气缸顶的距离是气缸高度的
,活塞b在气缸的正中央。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049291987823.jpg)
(ⅰ)现通过电阻丝缓慢加热氮气,当活塞b升至顶部时,求氮气的温度;
(ⅱ)继续缓慢加热,使活塞a上升,当活塞a上升的距离是气缸高度的
时,求氧气的压强。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929166314.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049291987823.jpg)
(ⅰ)现通过电阻丝缓慢加热氮气,当活塞b升至顶部时,求氮气的温度;
(ⅱ)继续缓慢加热,使活塞a上升,当活塞a上升的距离是气缸高度的
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929213362.png)
(ⅰ)320K(ⅱ)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929229528.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929229528.png)
试题分析:(ⅰ)活塞b升至顶部的过程中,活塞a不动,活塞ab下方的氮气经历等压过程,设气缸A的容积为V0,氮气初始状态的体积为V1,温度为T1,末态体积V2,温度为T2,按题意,气缸B的容积为V0/4,由题给数据及盖吕萨克定律有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049292601107.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929276905.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929291710.png)
由①②③式及所给的数据可得:T2="320K" ④
(ⅱ)活塞b升至顶部后,由于继续缓慢加热,活塞a开始向上移动,直至活塞上升的距离是气缸高度的1/16时,活塞a上方的氮气经历等温过程,设氮气初始状态的体积为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929307370.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929322364.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929338422.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929354410.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929369613.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929385503.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929400756.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929416690.png)
由⑤⑥式可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004929432694.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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