A piece of copper has a temperature of 73.6 C. When the metal is placed in 96.2 grams of water at 17.1 C, the temperature rises by 5.1 C. What is the mass of the metal?

103.8 g

Explanation:

When the hot piece of copper is placed in the water at lower temperature, the piece of copper gives off thermal energy to the water; as a result, the temperature of the copper decreases while the temperature of the water increases, until they both reach the equilibrium temperature.

The heat given off by the piece of copper is equal to the heat absorbed by the water, so we can write:

where:

is the heat absorbed by the water, where

is the mass of water

is the specific heat of water

is the rise in temperature of the water

Solving,

is the heat released by the copper, where

is the mass of copper

is the specific heat of copper

is the initial temperature of copper

is the equilibrium temperature

Solving for the mass,

Explanation: