$17\mathrm{.}35$ A $500\mathrm{.}0$ g chunk of an unknown metal, which has been in boiling water for several minutes, is quickly dropped into an insulat ing Styrofoam beaker containing $1\mathrm{.}00$ kg of water at room temperature $120\mathrm{.}0$C$2.$ After waiting and gently stirring for $5\mathrm{.}00$ minutes, you ob serve that the water$$s temperature has reached a constant value of $22\mathrm{.}0$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.