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So if you had a high temperature, this a small compared to b. If you're negative which means that dT/dp at constant H is less than zero.
高于反转温度，这一项相比于b很小,意味着H恒定时,偏T偏p小于零。
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dV dT Is equal to minus dV/dT at constant pressure.
它等于，负的恒定压强下的。
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This makes sense; the rate at which the cell population is growing, the derivative dX/dt, is proportional to the number of cells I have.
这个说的通,细胞数目的增长速度,就是导数dX/dt,和细胞数目呈比例关系
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SdT This has minus T dS minus S dT, but the dT part is zero because we're at constant temperature.
这一项包含负的Tds和，但是dT的部分等于零,因为温度为常数。
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dG/dT That is, this is, dG/dT at constant pressure.
这就是恒定压强下的。
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p So dV/dT at constant pressure is just nR over p.
所以恒定压强下dV/dT等于nR除以。
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du/dV So now our du/dV, dp/dT at constant T is just T times dp/dT which is just p over T minus p, it's zero.
现在我们的恒定温度下的，等于T乘以dp/dT，在这里,等于p除以T，最后再减去p，结果是0。
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du/dT And we discover that du/dT at constant V T is equal to du/dT at constant V.
可以发现恒定体积下的,等于恒定体积下的偏u偏。
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Well, we already know what dA/dT at constant V is.
我们知道恒定体积下的。
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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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V So it's minus T dV/dT at constant p, plus V.
负的T乘以恒定压强下dV/dT，再加上。
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T So we know that T dS/dT at constant volume is Cv over T, T and dS/dT at constant pressure is Cp, over T.
在恒定压强下定压比热容Cp乘以dT除以,所以在恒定体积下dS/dT等于Cv除以，在恒定压强下dS/dT等于Cp除以。
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T It's Cp dT over T at constant pressure.
定容比热容Cv乘以dT除以。
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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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