题目内容
(7分)横截面积为S的导热气缸竖赢放置在水平地面上,两个轻活塞A和B将气缸分隔为I、Ⅱ两个气室,两活塞问距离为d,两气室体积之比为l:2,如图所示。在保持室温不变的条件下,缓慢在活塞A上加细沙,使之向下移动一段距离h=
d。不计活塞与气缸壁之问的摩擦,室内大气压强为
,求所加细沙的质量。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040320267234.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004031979338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004031995345.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250040320267234.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032042618.png)
试题分析:由于是轻活塞,质量不计,活塞与气缸间摩擦不计,因此两部分气体压强相等,状态1时,气体压强等于大气压强
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032057424.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032089550.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032104722.png)
设所加细沙的质量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032120337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032135353.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032167816.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032182828.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032182818.png)
由于保持室温不变、气缸导热和缓慢加沙,气缸内气体作等温变化,由玻意耳定律得
p0dS= p′(d-h+ h′)S ①(2分)
p02dS= p′(2d-h′)S ②(2分)
联立①②式得h′=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032198327.png)
③代入②解得m=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004032042618.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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