Lake ice is safe to walk and skate on at about 6 cm thick. Lake Carnegie (Princeton's rowing lake) only freezes over deep enough for skating every couple of years. Assume, one night the air temperature drops to a steady T_[cold]. How long would this low temperature have to last to freeze the lake safely?
a. Make a thorough drawing of the situation after some ice x, about half of the required thickness) has already formed. Also, indicate the next thin (( Δ x )) layer of water which will freeze next.
b. How much heat needs to be removed per area from that thin layer to freeze it?
c. How much heat is conducted per area per time through the already formed layer of ice?
d. How long does it take to freeze the lake to a thickness of L?