Chapter 1.6, Problem 41P

To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water $\left(100°C\right),$ then is quickly transferred into a Styrofoam cup containing 250 g of water at $20°C$. After a minute or so, the temperature of the contents of the cup is $24°C$. Assume that during this time no significant energy is transferred between the contents of the cup and the surrounding. The heat capacity of the cup itself is negligible.

1. How much heat is gained by the water?
2. How much heat is lost by the metal?
3. What is the heat capacity of this chunk of metal?
4. If the mass of the chunk of metal is 100 g, what is its specific heat capacity?