1. A pond with a flat bottom has a surface area of 798 m2 and a depth of 3.0 m. On a warm day, the surface water is at a temperature of 25°C, while the bottom of the pond is at 12°C. Find the rate at which energy is transferred by conduction from the surface to the bottom of the pond. (Use 0.6 J/s · m · °C for the thermal conductivity of water.)
2. An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C. A 440-g sample of silver at an initial temperature of 85°C is placed in the water. The stirrer is used to stir the mixture gently until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup.