The fracture strength of glass may be increased by etching away a thin surface layer. It is believed that the etching may alter the surface crack geometry (i. e. reduce crack length and increase tip radius). Calculate the ratio of the etched and original crack tip radii if the fracture strength is increased by a factor of 4 when 63.0% of the crack length is removed.

Asteam is contained in a rigid tank with a volume of 1 m3. initially, the pressure and temperature are 7 bar and 500 oc, respectively. the temperature drops due to cooling process. determine: (1) the temperature at which condensation begins in °c, (2) the fraction of the total mass that has condensed when the pressure decreased to 0.5 bar. (3) the volume in m3 occupied by saturated liquid at the final state?