A foam cooler of negligible mass contains 1.75 kg of water. Ice from a refrigerator at −15°C, is then added to the water in the cooler. When thermal equilibrium has been reached, the total mass of ice in the cooler is 0.778 kg. Assuming no heat exchange with the surroundings, what mass of ice was added? For water, Lf = 334 × 103 J/kg, and for ice, ci = 2100 J/(kg • K).

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

Because air contracts as it cools, the air pressure inside a freezer is typically lower than on the outside. why do ice cubes inside a freezer tend to shrink over time? a. the ice dissolves oxygen from the air, forming a denser crystalline matrix. b. the ice reacts chemically with carbon dioxide in the air, forming gaseous carbon compounds. c. the ice melts, and then the liquid freezes as ice crystals on the bottom of the freezer. d. the ice sublimes, and then the water vapor deposits as ice crystals on the sides of the freezer.

What is the freezing point of radiator fluid that is 50% antifreeze by mass? kf for water is 1.86 ∘c/m.