After watching this video at the end when he gave the example of PV=nRT and he explained that T and n decreases he went on to explain P and V. Prior to this I would have thought that the ideal gas equation required all but one unknown variable to check if the unknown variable has either increased, decreased or remained the same. However, from his example he shown that this is not the case. So can we relate the effects on temperature say now we have a can of boiling water and we cool it down. So now we know that T and n decreases. So the left hand side P times V should decrease. So would I use the variable T of average velocity. So I would say that the pressure increases as the number of collisions per unit time decreases and so does the force per collision. so as a result of that there is a net force pushing the can out in. So the V increases too. But now thinking about this, after increasing my temperature and number of moles of gas, the PV definitely should increase. So I'm thinking if volume increases could the pressure remain constant? Cos now if I combined the laws and give as n and T increase and V would increase where P remains constant. Or I could also have a case where P is not constant so the 'stress' is more evenly distributed between the decrease in pressure and volume as he described in the example. So actually, would I still need only one variable? So in the video now that PV=nRT and since nRT decreases so PV would have to decrease. So now we know for sure that the V decreases as it is shown that it contracts. But how can we also be sure that the pressure drops? Perhaps the pressure remained the same or it could be that the volume and pressure decreases as he'd described. I think using the temperature and number of moles decreasing to explain that P drops would be the intermediate explanation. So it would be something like: as the T and n decreases the pressure would drop. Then after saying that, we should explain that the atmosphere exerts a net force causing it to shrink. So when it shrinks the pressure would increase to either A) the amount it once was or B) increase to a amount lesser than the initial amount. So in this manner of explanation the ideal gas law's variable on the left hand changes constantly but they still multiply to get the same reduced nRT. But the final state of the PV could have 2 possible end product. But could there be a 3rd product where the V decreases so much that P actually increases? I don't think so right? Because that would mean the can continues to contract even after there is no net force. So this would break newtons 2nd law because if it shrinks any further the internal pressure>external pushing it out again. So actually only 2 scenarios are possible even thought mathematically 3 scenarios are possible? And actually what would be the reason for why the P would not remain constant? I agree that mathematically it makes sense. But if I look at the forces, the pressure is smaller so they would want to have equal external and internal pressure. So shouldn't it contract until Pexternal=Pinternal? What would allow the Pexternal>Pinternal? Could it be that the can being slightly rigid would stop it from getting crushed so the V doesn't continue decreasing? If so what enables the rigidity of the can to prevent it from being further compressed? Because I thought in terms of forces, the can shouldn't be able to push the external pressure away by itself (the only forces acting on it are the external atmosphere and internal gases) so I don't really understand how and why this 'rigidity' comes in actually. So essentially, how can we say for sure than both the pressure and volume decrease and not just volume decreases? Thanks :) and let me know if I'm vague at some parts.