-
And you already saw last time there was this relationship between the temperature and volume changes along an adiabatic path.
是条绝热路径，而上次你已经看到,沿着绝热路径温度和体积,的变化有这个关系。
-
Because we did work at constant pressure, and so it's just volume difference times pressure.
因为是在恒压下做功，所以功就等于体积变化乘以压力。
-
As it does that it changes the volume of the heart and gives the - creates the pressure that moves blood around your body, so it has that muscular system.
这使心脏的体积发生变化,产生了足以使血液流遍全身的压力,这就是心脏中有肌肉系统的原因
-
And the equation of state, pressure versus volume at constant temperature, is going to have some form, let's just draw it in there like that.
系统的态函数，恒温下压强比体积，变化曲线，就像这样。
-
But now, what happens if, instead we look at what happens when we go to some state one to some other state two and it's the pressure. Or the volume, that changes.
但是现在，我们看看如果,我们关系从状态一变化到状态二时,体积或者压强发生变化。
-
We know how the volume and temperature vary with respect to each other at constant pressure.
知道在恒定压强下,体积如何随着温度变化。
-
You know how pressure changes with temperature at constant volume if you know the equation of state.
如果你知道状态方程,知道在体积恒定的时压强如何随着温度变化。
-
Then the second derivative gives the change in entropy with respect to the variable that we're differentiating, with respect to which is either pressure or volume.
二阶导数给出熵,随着变量变化的情况，这些变量包括压强或者体积。
-
This depends on the path. It tells you right here the path is constant pressure. These don't depend on the path, right. V doesn't care how you v get there. u doesn't care how you get there.
这由变化的具体路径决定,这个小脚标表明过程是恒压的,这些量都与具体路径无关,即不管是通过什么路径使得体积变化为Δ
-
The volume is going to change, and we can see how the entropy changes.
体积发生变化，然后看熵如何发生变化。
-
And so here the volume can change.
体积会发生变化。
-
The additional change due to changing pressure volume is certainly measurable.
由于压强和体积的改变带来的,附加变化无疑是可以测量的。
-
So I need, well the pressure is constant, but there's a change in volume.
压强不变，体积变化。
-
Can determine how entropy is going to behave as the volume changes.
这些偏导数,你就可以知道当体积变化时熵如何变化。
-
OK, now we actually would like to simplify this or to write this in terms of not the volume change, v2/v1 but the pressure change. So, we have V2 over V1.
接下来我们将要把问题简化,不用体积变化来描述，而改作用压强变化来描述，现在我们有。
-
We discovered that the quantity dA, under conditions of constant volume and temperature, dA TS And A is u minus TS.
我们发现在恒定的体积和温度下，亥姆赫兹自由能的变化，小于零，is，less，than，zero。,亥姆赫兹自由能A等于内能u减去。
-
In other words, the order of taking the derivatives with respect to pressure and temperature doesn't matter And what this will show is that dS/dp dS/dp at constant temperature, here we saw how entropy varies with volume, this is going to show us how it varies with pressure.
换句话说,对温度和压强的求导顺序无关紧要,结果会表明,恒定温度下的，对应我们上面看到的，熵如何随着体积变化，这个式子告诉我们，熵如何随着压强变化。
应用推荐