Now, if this is an ideal gas, we know that pressure is equal to nRT over volume.
如果这是一个理想气体系统,我们知道压强等于nRT除以体积。
And so, we can rewrite this as the work nRTln is equal to minus nRT log p1 over p2, nRTln or nRT log p2 over p1.
因此我们可以把这个式子改写一下,功等于负的,或者。
Remember the equation of state for Van der pV=nRT Waal's gas is not pV is equal to nRT, but p plus the attraction term.
记住范德瓦尔斯气体的状态,方程不是,而是p加上一个吸引项。
pV=nRT And so of course it's still pV equals nRT.
显然状态方程仍然是。
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。
And so we can write this, ln minus nRT log V2 over V1.
所以结果是,负的nRT除以。
The ideal gas constant doesn't change, temperature doesn't change, and so v we just have minus nRT integral V1, V2, dV over V.
理想气体常数不变,温度也不变,因此,是负的nRT,积分从v1到v2,dv除以。
So instead of p, here I'm going to put nRT over V.
于是把p写成。
v dv We have minus V1, V2, nRT over V dV.
负的v1,v2,nRT除以。
p1/p2 So, the nRT's cancel, and we have p1 over p2.
因此nRT相消,结果就是。
So what happens then we're going to use the ideal gas law. So it's approximately delta u plus delta nRT. That's a constant. That's a constant.
我们现在要应用理想气体物态方程,这个近似等于ΔU加上Δ,这是常数,这是常数。
nRT So we have pV is nRT.
对理想气体,我们有pV等于。
应用推荐