An ideal gas is taken from a to b on the pV-diagram shown in Fig. E19.15. During this process, 700 J of heat is added and the pressure doubles.

(c) How does the internal energy of the gas at a compare to the internal energy at b? Be specific and explain.

Video transcript

Hey everyone welcome back in this problem. We have an ideal gas that follows the process shown in the PV diagram below The gas absorbs 960 jewels of heat to triple its pressure during the process. Okay, we're asked what is the relationship between the internal energy at point X. To the internal energy at point Y. Okay. All right. Now we see from our diagram or PV diagram that we have a vertical line between point X and Y. Okay, this vertical line means that we have constant volume. Okay, the volume is not changing. And what do we know if we have a constant volume process? If we have a constant volume process, this means that the work is equal to zero and delta U. Is therefore equal to Q. Or the heat. Okay. All right. So we have a vertical line we're saying that means constant volume. The volume is not changing. That tells us the work is zero. Which tells us the internal energy is equal to Q. Okay, well, what we're trying to find is the internal energy okay. From point X to point Y. Well, the change in internal energy delta U. Between X and Y. We're told the gas absorbs jules. Okay. And so Delta U. Is going to be 960 jewels, this means that you why minus U. X. Is equal to 960 jewels. Okay, that change in internal energy. And so when we look at the difference between UI and UX it's going to be exactly 960 jewels. And so we're gonna have answer. E. Now, this also says that Delta U. Is equal to the heat absorbed by the gas, which is exactly what we found, right? Alright, So we have answer. E. The internal energy at point Y minus the internal energy at point X is equal to 960 jules. Okay. In Delta U. Is equal to the heat absorbed by the gas. Thanks everyone for watching. I hope this video helped you in the next one.