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"You know the thickness, tolerances of wood has to be exactly right for the right tone, and volume of a soundboard has to be measured exactly, and that's done mostly by ear.
VOA: standard.2010.07.06
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We could just collect a bunch of data. For a material .What's the volume it occupies at some pressure and temperature?
对一种物质我们可以得到一系列测量数据,在给定的温度和气压下,它的体积是什么？
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And we combine this with first law, which for the case of pressure volume changes we write as this.
结合第一和第二定律,对于压强体积功我们可以这样写。
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Different amount of metabolic activity because one has a greater volume of cytoplasm than the other, for example, so these are exactly the right kinds of ideas.
大小不同,代谢活动的总量就会不同,可能因为一个细胞的胞质比另一个体积大,以上这些观点都是非常正确的
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So for the reversible process, the work done is the integral under the pressure volume state function, the function of state.
对可逆过程，做的功,是压强体积态函数曲线下，的积分面积。
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That for an ideal gas it has to be the case that there's no volume dependence of the energy.
我们可以直接推导这个结果,即证明对理想气体，内能和气体体积无关。
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You're allowed Cv comes out here for this adiabatic expansion, which is not a constant volume only because this is always true for an ideal gas.
绝热过程写下,这个式子是因为它对理想气体都成立，并没有用到等容过程的条件,只用了理想气体的条件。
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For instance, the pressure and the temperature, or the volume and the pressure.
比如压强和温度，或体积和压强。
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So that you could see that for the ideal gas, u would not be a function of volume, but only of temperature.
所以我们可以看到对理想气体，内能不依赖于体积，而仅仅是温度的函数。
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You just change volume to pressure and basically you're looking at enthalpy under a constant -- anything that's done at a constant volume path with energy, there's the same thing happening under constant pressure path for enthalpy.
可以看到这就是把体积换成了压强,一般我们都是在一种恒定状态下,考虑焓的，任何在恒容条件下,能伴随能量变化的东西，也在恒压条件下伴随焓同样地变化,所以你可以经常。
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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。
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dw=0 Well for constant volume, dw is equal to zero.
约束是恒定体积，此时。
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We have discovered that this partial derivative that appears in the definition, the abstract definition of the differential for internal energy, is just equal to the constant volume heat capacity.
我们还发现,这个偏微分出现在了，内能的偏微分,定义式中，它也就是热容。
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OK, for constant volume, this is zero.
对于恒定体积过程，第二项等于零。
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For instance, the volume.
比如体积。
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But because in many cases we can reasonably either model or measure equations of state, collect data for a material for its temperature, pressure, volume relations, then in fact if we can relate all these quantities to those then in fact we really can calculate essentially all of the thermodynamics. For the material.
但是因为在很多情况下,我们能够合理的给出状态方程的模型,或者通过收集一个物质的，温度，压强和体积之间的关系,来测量其状态方程，所以实际上我们可以给出压强等物理量,和热力学势之间的关系,并计算出所有的热力学势，对于给定的物质。
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nRT So, dp/dT, for our ideal gas, at constant volume, remember pV is nRT.
对于理想气体状态方程pV等于，所以对理想气体。
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So this isn't the most useful form that we can have, but what we'll see shortly is that from this, we can then derive further criteria for essentially any set of variables or any set of external constraints, like constant temperature or pressure or volume and so forth that we might set.
所以这不是我们所能得到的最有用的形式，但是我们会很快看到，我们能够进一步推导出包含任意变量,或者任意约束的自发过程判断标准，比如说恒定的温度，压强,体积或者其他我们能够给出的约束。
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I also want to assume for our present purposes that there's only pressure volume work going on, which is to say I want to put pdV p dV in here minus p dV for dw.
同时假定,对于我们目前的目的而言，只有压强做功这就是说,我要把这里的dw替换为负。
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For the ideal gas, we know that u is volume independent.
对于理想气体,我们知道u与体积无关。
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If you have a real gas and you write du is Cv dT and your path is not a constant volume path, then you are making a mistake. But for an ideal gas, you can always write this. And this turns out to be very useful to remember.
对于真实气体，如果其变化过程,不是恒容的，du=Cv*dT就不成立，但对于理想气体,这条规则永远成立,这一点非常有用，请记住。
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OK, so for a constant volume process, du we can write du, partial derivative of dT u with respect to T at constant V, dT, dv plus partial derivative of u at constant V, dV.
好，对于一个恒定体积的过程，我们可以写出,等于偏u偏T，V不变，加上偏u偏V，T不变。
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