The seed crystal used for czochralski crystal growth is necked down to about 3 mm diameter to produce a dislocation-free crystal. use 2 x 10^6 g/cm2 as the yield strength of silicon at the growth temperature (the units are strange but correct assuming the gravitational constant of earth, etc.) and determine the maximum length of each ingot that can be supported by this neck if the ingots are 150, 200 and 300 mm diameter.
for the 200 mm diameter case, how many wafers can be produced (if the final wafer thickness is 725 mm).

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?