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OK, now, we're going to look at the internal energy, and we're going to pretend that it is explicitly a function of temperature and volume.
好，我们接下来看看内能，我们假设,它是温度和体积的函数。
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It is essentially equal to internal energy for condensed systems, but when you look in the books sometimes they will use this term.
它与内能是相同的,在凝聚体系中，在你看书时有时你会发现,它们会这样使用。
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But it's allowed to say the internal energy is a function of temperature and volume.
但是我们也可以说内能,是温度和体积的函数。
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And, so you propose that there is no, that this derivative is zero, and that the internal energy is given simply by this quantity.
你认为这是零，这个微分是零，内能仅仅由,这个简单的量决定。
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So, we have, we're interested in the change in internal energy for various experimental constraints.
我们感兴趣的是,在各种实验环境约束下内能的改变。
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One is, du, u is called the internal energy dw or just the energy, is equal to dq plus dw.
其中一个是：du，u是内能,或能量，等于dq加上。
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And so for many, many problems, especially on exams, especially on this first exam, you will be able to say that this is the relationship between internal energy and temperature.
对于很多问题，特别是考试中的问题，你们要能够说出来,这是内能与温度的关系。
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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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The value of the internal energy is only determined by temperature.
内能的值,只与温度有关。
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And the first law says, well heat and work are different forms of energy, and we can add them, and the path dependence of these two things is somehow cancelled in the fact that we have this internal energy.
热力学第一定律说，热和功是能量的不同表现形式，我们可以把它们加起来,它们与路径相关的部分相互抵消,我们就有了内能。
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There's some energy, some internal energy.
它包含一些能量。
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We'll then look at the quantity, internal energy, which we define through the first law, and we think of it as a function of two variables T and V.
接下来我们考虑内能，这是由热力学第一定律定义的物理量，我们把它看作T和V的函数。
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And because there is an explicit relationship between u, delta u, q and w, you can always find the easy way to derive the change in internal energy or the heat or the work.
因为Δu，q和w之间,有明确的关系，一般来说,内能或热或功的变化,易于计算。
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