Water flowing at $0\mathrm{.}01k\frac{g}{s}$ pssses through a $1$ cal dixmeter chin salled cube which is immersed in a bach of crushed loe sod wrater such chst the wall temperature may be assumed to be $I_0=0C.$ The inlet vater camperscure $I_1=40C$ and the outlet vater temperature $I_0=6C.$ The tube is long enough thst the flow ceg be acoumel to be frilly deweloged both hydinodymendeally snd therrally over the lengch of the tube. Calculate the cotal rate at which hest is cransfecred between the strean of water and the cooling bath sod decernine the lengch of che cube required to effect the rate of heat transfer under these condiclons.