## Problem 5.48

#### Two solid objects, A and B, are placed in boiling water and allowed to come to temperature there. Each is then lifted out and placed in separate beakers containing 1000 g water at 10.0 oC. Object A increases the water temperature by 3.50 oC; B increases the water temperature by 2.60oC.

(a) Which object has the larger heat capacity?

To analyze this problem, we have to focus on how much heat was transferred from each of the objects to the water. Both objects were initially at 100oC (the boiling point of water), and were both placed in the same mass of water. Object A raised the temperature of the water more than did object B. Therefore, we have to conclude that more heat was transferred from A to the water than from B to the water. Since A and B were at the same starting temperature, we must conclude that A absorbed a greater quantity of heat in reaching 100oC than did B. Heat capacity is the ratio of heat to temperature change,

C = q/DT

So if A absorbed a larger amount of heat for the same temperature change (we know this because A transferred more heat to the water than B), then A must have a larger heat capacity than A. (Of course, this assumes that A and B were at the same temperature before they were placed into the boiling water.)

(b) What can you say about the specific heats of A and B?

Specific heat is just the heat capacity per gram. Since we don't know the masses of the objects, we can't really say anything about the specific heats. Sneaky question.