Related rates problem from my ancient calculus memory:  you know how fast the radius of your snowball is shrinking; you want to know how fast the volume of the snowball is shrinking.  (The rates are related — hence, related rates problem.)  Applet and explanation here.  (I also remember a similar quiz problem about an oddly-shaped sink with water level falling at a given rate.) 
The phase transition I’m waiting on at the moment is the evaporation of water from my clothes.