A 500.0-g chunk of an unknown metal, which has been in boiling water for several minutes, is quickly dropped into an insulating Styrofoam beaker containing 1.00 kg of water at room temperature (20.0o C). After waiting and gently stirring for 5.00 minutes, you observe that the water’s temperature has reached a constant value of 22.0o C. (a) Assuming that the Styrofoam absorbs a negligibly small amount of heat and that no heat was lost to the surroundings, what is the specific heat of the metal? (b) Which is more useful for storing thermal energy: this metal or an equal weight of water? Explain. (c) If the heat absorbed by the Styrofoam actually is not negligible, how would the specific heat you calculated in part (a) be in error? Would it be too large, too small, or still correct? Explain.
Solution 39E Heat comes out of the metal into water. The final temperature is in the range 0 < T < 100 C 0 a)Q + Q = 0 water metal m water waterT water+ m metal metal metal= 0 0 0 1 kg × 4190 J/kg.K × 2 C + 0.500 kg × c metal× 78 C = 0 0 cmetal= 1 kg×4190 J/kg0K×2 C 0.500 kg×78 C =215 J/kg.K Specific heat of the metal is 215 J/kg.K b)Water has a larger specific capacity so stores more heat per degree of temperature change. c)If some heat went into the styrofoam then Q metalhould actually be larger than in part(a), so the true metal is larger than we calculated, the value we concluded would be smaller than t5he true value.