FYKOS Year 32 Series 5 Problem 2 — warm reachability into the ball · FYKOS 32 #32.5.2
Physics · thermodynamics
Problem
Imagine you have subcooled homogeneous metal ball that you have just taken out of a freezer set to very low temperature. You want to find out how fast the ball temperature will increase if you put it in a warm room. It would be a university-level problem. Because of that, we made it easier for you. We ask about how deep into the ball will the „warm area“ reach. You can estimate it using dimensional analysis. We know relevant parameters of the ball - its density [ρ]=\jdkg.m−3, specific heat capacity [c]=\jdJ.kg−1.K−1, thermal conductivity of the ball [λ]=\jdW.m−1.K−1 and we are interested in dependence on time [t]=\jds.