Heating of two identical balls You are given two identical steel balls of radius (say) 5 cm. One ball is resting on a table, the other ball is hanging from a string. Both balls are heated (with a blow torch) until their radii have increased to the same value of 5.01 cm. Which ball absorbed more heat and why?
 A: Part of the heat absorbed becomes internal energy, while the other part becomes gravitational potential energy. The gravitational energy of the two balls changes in opposite ways when the radius is increased. Then to make the two balls have the same internal energy, different amounts of heat are needed...
A: Not-so-great question from the prof.
What is the table made of? 
If the table is 1cm thick brass it would absorb quite a bit of heat from the ball resting on it (and also be quite an awesome table). If it is glass there will be very little heat transfer. If there is a block of aerogel or space shuttle tile under the ball there will be nearly zero conductive loss, and not that much convective loss as the table will obstruct the airflow far more than the free-hanging one.
A 10cm steel ball weighs about 4kg - if the string breaks (or catches on fire) and it lands on the table it will have the same heat loss as the one already there. If the glass table breaks after being smacked by a big steel ball falling on it you will have 2 hot balls of metal on the floor, also sharing the same thermal conditions. If it rolls off the brass table and finds a quiet corner with no airflow it may retain more heat than the table-dwelling sphere.
