Water at its freezing point (ti, pi) completely fills a strong steel container. the temperature is reduced to tr at constant volume, with the pressure rising to pf (a) show that the fraction y of water that freezes is given by v-v (b) state explicitly the simplifying assumptions that must be made in order that y may be written v" [2"(t,- t) - "(p,- p) i= 0°c, 1.01 x 105 pa; f= -5°c b"67 x 10-6 k-1; k" = 12.04 x 10-1" pa-; v- vf= -1.02 x 10-4 m3/kg. 5.98 x 107 pa

Consider a small frictionless puck perched at the top of a fixed sphere of radius r. if the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere? [hint: use conservation of energy to find the puck's speed as a func e conservation of energy to find the puck's speed as a function of its height at what value of this normal force does the puck leave the sphere? ] here on the puck.