题目内容
(9分)一定质量的理想气体被活塞封闭在竖直放置的圆形气缸内,汽缸壁导热良好,活塞可沿汽缸壁无摩擦地滑动。开始时气体压强为p,活塞下表面相对于气缸底部的高度为h,外界的温度为T0。现取质量为m的沙子缓慢地倒在活塞的上表面,沙子倒完时,活塞下降了h/4。若此后外界的温度变为T,求重新达到平衡后气体的体积。已知外界大气的压强始终保持不变,重力加速度大小为g。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004924455945.png)
试题分析:气缸导热良好,说明气体温度一直等于外界温度T0,设气缸底面积为S,活塞质量为m0,大气压强p0
开始平衡时有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004924471760.png)
沙子倒完后平衡时,对活塞分析
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004924502839.png)
整理可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004924518736.png)
根据理想气体状态方程有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004924549995.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004924564578.png)
联立可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004924580719.png)
外界温度变为T时,根据理想气体状态方程可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049246111066.png)
根据活塞平衡可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004924627854.png)
重新平衡后的气体体积
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049246421323.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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