Now, suppose I took this two paths, and I took -- couple them together with one the reverse of the other.
其中一条的方向反过来,这是初态,末态,路径1,先冷却。
We want to integrate. So let's take the integral of both sides, going from the initial point to the final point.
分别从初态,到末态做积分,消去微分。
For example, if you started here and you did all this and you came back here, the average velocity would be zero, because you start and end at the same value of x, you get something; 0 divided by time will still be 0.
例如,如果你从这里开始运动,经过这个过程又回到这里,平均速度就是0,因为初态和末态的位移相同,你得到了什么呢,0除以时间还是0
So, the first obvious one is to take V1 to V2 first with p constant. So take this path here.
从初态到末态可以有无数种路径2,甚至像这样,我们只研究两种。
That's the work that the system is doing to the environment. I'm doing work to the environment. The work is negative, which means that work is being done to the environment.
功的大小,就是矩形的面积,这样我们就实现了一台热机,冷却,加热,加热,冷却,系统回到了初态。
So there's going to be a line that's going to connect the initial point to the final point, and that line mathematically is not going to be the same as this one here.
连接绝热过程,初末态的曲线的方程,和等温线的方程,也不会相同。
So if I take p times V to the gamma, anywhere on the path, it's going to be equal to the same relation This is going to be true for any point on the path.
结果都,将等于,初态点的,只要在这条路径上。
OK, you use the ideal gas law, etc., then you get a relationship that connects the pressure and the temperature, like here we got a relationship that connected the temperatures and the volumes together.
我们会得到,一个联系初末态,的压强和温度的,关系式,就像这个联系过程中。
This is going to be the connect, what connects the pressures and the temperature.
这就是联系初末,态压强和温度的关系式。
If it was non-reversible, I would be allowed to put an initial point and a final point, but I wouldn't be allowed to put a path between them like this, connecting them together.
如果是不可逆过程,我可以画出过程的初态点,和末态点,但是我不能再像这样,画出连接这两个点的,路径曲线来。
Define the initial state. Define the final state.
定义初态,定义末态,定义路径。
It only cares about the end points.
于初末态。
And if I draw a diagram on a T-V diagram of T-V V1 I'm starting with some V1 here.
画出过程的,图,what,I’m,doing,here,初态是。
p1 V1 Initial find -- there are many ways p2 V2 V1 I can get from one state to the other.
初态的氩气状态为,末态为。
and final points, a relationship between the temperature and volume for the initial and final points.
我们就得到了,初末态的温度,和体积间的关系。
This is very different from the functions of state like pressure and temperature.
联系初末两态的整个过程,这与压强。
How do you get from the initial state to the final state?
你是怎样,从初态过渡到末态的?
You could take a continuous path, where you have an infinite equilibrium points in between the two, a smooth path, whereyoudrop pressureand temperature simultaneosly in little increments.
你可以选择光滑的连续路径,在初末态间有,无数个平衡态的点,压强和温度同时一点,一点地下降。
So I'm starting right here.
我从初态。
It's the pressure the external world is applying on this poor system here.
V是气体初态和,末态的体积之差。
What is y-y0? The final y is 0, the initial y is 15. You solve for that equation and you will find the final velocity.
-y0是什么,末态的y是0,初态的y是15 你们已经得到,然后你可以找到最终速度
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