I have two questions on fine points of thermal physics. 1. Is an isotropic solid's volume-expansion coefficient beta exactly equal to 3 times its linear-expansion coefficient alpha, or is it only approximately equal? Some textbooks (Fischbane, Walker, Young) say the relation is exact, while others (Giancoli, Katz) say it's approximate. It's also possible to find books that say it's approximate, such as https://books.google.com/books?id=SwsNbiMDqzcC&pg=PA100 . In poking around the Web, I can't find anything that gives sufficiently precise experimental data or that gives anything but the simple argument about differentiating a cubic function--which I don't see anything wrong with, so why wouldn't it be exact. (Technically these constants are defined only in the limit of small temperature changes, right?) 2. Someone told me that the rate of heat transfer by convection typically saturates as Delta T increases, but didn't have any further information. I can't imagine why it would. Does anyone know anything about that? I'd appreciate any information or any sources, especially those that don't require access to a university library.