Hello, this video is the first in a series of videos that talk about ideal gases. I think we all know or think we know what an ideal gas is, we deal with it all of the time. However, it turns out that we can treat some other things as ideal gases as well including electron gases and photons, but we will get to that in due course. We start by reminding ourselves of the ideal gas law PV = NRT. This was first presented by Jacques Charles in the long time ago. He lived from 1746 to 1823 and he studied the behavior of gases among other things. More formally, ideal gases exist in the domain where the Maxwell-Boltzmann limit holds. And this is a limit where the particles are on average are far enough apart that they don't really interact with each other except briefly during collisions. The collisions are necessary to establish thermodynamic equilibrium, but on average, they don't feel the effect of each other. So just a reminder that this is the Maxwell-Boltzmann partition function. And if you factor out the gamma term, then you get this sum called Q, the third equation on the slide, which is a sum over k, which is a quantum state index e to the minus beta epsilon k where epsilon is the energy. This is called the molecular partition function and it's a function only of molecular properties and temperature through beta which is, remind you is 1 over kt. So first we assume that we could separate the translational and internal energy modes of the molecule. And this is the substance making up the gas and this is a reasonable assumption if there are no external fields operating on the gas. So we write that epsilon, the energy is the translational energy plus the internal energy. Now if we just note in general that e to the sum of two numbers a plus b is equal to the product of e to the a times e to the b. And if a and b are independent of each other, that is changing a doesn't necessarily affect b, then we can write the sums as shown in the last slide, the sum over a and b of e to the minus a times e to the minus b. And that can split into two sums the sums a e to the minus a and e to the minus b. So that allows us to write the partition function at the log of the partition function more formally as e to the minus alpha times the sum of the e to the minus beta epsilon for translation times the sum for internal motion. So that the length of the Maxwell-Boltzmann partition function, lane of the partition function is e to the minus gamma times the translational molecular partition function nv times the internal molecular partition function. And it turns out that the same argument applies to internal modes so that we can write the internal partition function as the product of the rotation vibration and electronic modes. And so therefore the problem of finding the fundamental relation for ideal gases devolves to finding the cues. Remembering that the the fundamental regression is equal to minus k in the partition function for whatever particular representation that you were in. Thanks very much and have a great day.