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Now, the coefficient that relates the amount of heat in to the temperature change is obviously going to be different for these two cases.
在这两个例子中,很显然联系热量和温度变化的系数,是不一样的。
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If I pick an angle of 60 degrees, these are some numbers like half and root 3 over 2.
要是我选择一个 60°的角,上面的系数就会是二分之一和二分之根号三
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And so instead of defining efficiency the way you've got it written there, I'm going to define what's called something different for a refrigerator which is called the coefficient of performance.
现在我们不用,效率的那个定义，我给出一个,有关制冷机的,新的定义,叫做制冷系数。
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And we can simplify this expression as saying negative e squared over 4 pi, epsilon nought r squared. Epsilon nought is a constant, it's something you might see in physics as well.
也会遇到它,在这里，你可以就把它,理解为一个转换系数,我们需要做的。
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And then the repulsive term, some positive coefficient r and r to a very high number.
然后排斥力，一些正系数,以及具有很大数值的。
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If there were perfect correlation, then it would be a correlation of one.
如果是完全正相关的，也就是相关系数等于一。
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So this is just going to be T2 over T1 minus T2, that's our coefficient of performance.
这就是我们的，制冷系数。
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And if that's equal to zero, that means that the Joule-Thomson coefficient for an ideal gas is also equal to zero. We're going to actually prove this later in the course.
说明理想气体的,焦耳-汤姆逊系数也等于0。,详细的证明过程,会在以后的课上给出。
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And we saw that, you saw that the Joule coefficient for an ideal gas was zero.
我们会发现，你们也会发现,理想气体的焦耳系数是零。
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Your numbers with the primes on them are related to mine by this relation.
你的带撇的系数,与我的系数的关系由这个式子确定
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This is the proportionality that is multiplied by the quantum.
这就是与量子的,比例系数。
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Right? In other words I've got the stoichiometric coefficients in there and the values, and I'm subtracting the reactants from products -1652kJ/mol wind up with minus 1652 kilojoules per mole.
对吧？换句话说这里我用了化学,计量系数和生成热的值，从生成物中减去反应物,最后得到。
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I feel like I have to introduce concepts like variance and co-variance and correlation in order to talk about finance; so that's what we'll do in Lecture Two.
我会讲到像方差,协方差,相关系数,这样的概念,为金融学的内容作一些铺垫,我们会在第二课讲到
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How do I get your numbers in terms of my numbers?
我怎样用我的系数来表示你的系数呢
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If she's got a pair of numbers and you got a pair of numbers, the new numbers are called the primed numbers and you want to write them in terms of yours.
如果她有一组系数 你也有一组系数,新的系数被称作带撇的系数,你想用自己的形式来表示它们
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And you can find these compressibility factors in tables. If you want to know the compressibility factors for water, for steam, at a certain pressure and temperature, you go to a table and you find it.
各种气体的压缩系数,想知道水或者水蒸气,在某个温度和压强下的，压缩系数，查表就行了，这是实际气体状态方程的。
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but right now you're going to have to take it for granted. So, if the Joule-Thomson coefficient is equal to zero, just like we wrote, du = Cv dT du = Cv dT for an ideal gas, we're going to dH = Cp dT have dH = Cp dT for an ideal gas as well.
但是现在请你们应该把它看成理所当然的,所以，如果焦耳-汤姆逊系数等于零,就像我们写的，对于理想气体,我们也可以得到对于理想气体。
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.. The problem is again the ideal-- they're trying to work toward what I think of an ideal that we see in finance-- 1 mainly, the perfect correlation of consumption and the elimination of risk--we all help each other.
问题又回到了理想-,他们为之奋斗的这种理想状态,如果用金融学的理念来解读-,就是消费与风险消除的相关系数为,即完全正相关，所有人都互助互利。
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The reason it's low is that we do have,what I think is, superior diversification and that really lowers the University's risk.
我认为耶鲁beta系数低的原因是,我们有卓越的多元化投资,这确实降低了耶鲁资产的风险
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Therefore, it'll compress by an unknown x, which is equal to mg divided by the force constant of the spring.
因此它的压缩量为 x,也就等于 mg 除以弹簧的弹性系数
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And so they defined them, p after many experiments, the limit of this 0 delta T delta p and the limit of delta p goes to zero as the Joule-Thomson coefficient.
他们定义了这些量，以及它们的范围，ΔT比Δ,Δp的极限趋近于,叫做焦耳-汤姆逊系数。
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Over here, we have dq=Cp dT, the heat, the proportionality between heat - and temperature rise is given by this, the constant pressure heat capacity.
这里我有dq=CpdT，这是热量，这是联系热量,和温度变化的系数，恒压热容。
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If you want to know what the number c is, you say, let's put time t=0.
比如,如果你想知道系数c代表的是什么,我们令时间t=0
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When I give you multiple of i and another multiple of i, there's some has got as its coefficient the sum of the two coefficients.
如果我给你两个不同 i 矢量的倍数,就可以得到某个矢量,且它的系数是这两个系数的和
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of a stock is how much it reacts to movements in the market portfolio.
一只股票风险指标β系数直接反应出，The，β,市场组合变动与投资收益的相关性。
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I mean, with the b and c? What value should I pick?
我指的是b和c,这两个系数应该取什么值
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The first question is, what's the beta of the Yale portfolio?
第一个问题是,耶鲁投资组合的beta系数是多少
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This is real, unlike the Joule coefficient which is very small so that most gases have tiny Joule coefficients. So if you do a Joule experiment, you hardly measure a temperature change. With real gases, here you do actually measure it. You can feel it with your finger on your bicycle tire.
系数那样小以至于,大多数气体的焦耳系数,都很小，所以如果你做焦耳实验,很难测量出温度的变化,对于真实气体，你可以测量它，你能通过手指按在,自行车轮胎上来感觉到它。
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The claim is, I can write any vector you give me as a real scale i plus a real scale j.
也就是说,我可以把任何你给我的矢量,写成 i 和 j 的实系数线性组合的形式
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It will typically look like this and the formula we say is F = - kx, where k is called "The force constant."
图像看上去一般就像这样,对应的式子是 F = - kx,k 叫做"弹性系数"
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