1, imagine two identical and synchronized turkeys going towards each other. Where they meet gives the answer.
2, for uniform temperature, obviously true. If not uniform, forming "properly" two closed curves passing through the point of the lowest temperature and the point of the highest temperature will do. "Properly" here means to keep the temperature along the curve either statically climbing or dropping, that is, never to go up and down the "hills" or "valleys" except for the two points mentioned. Which can be done because of 单值连续 .
3, apparently one can apply 2. for showing the existence of such a molecule ( I still need to think it through), but, imagine the extreme case of two molecules which just switch positions at boiling... which seems to contradict the supposed answer. Perhaps I miss something here.
