Suppose that 0.48 g of water at 25 ∘ c condenses on the surface of a 55- g block of aluminum that is initially at 25 ∘ c . if the heat released during condensation goes only toward heating the metal, what is the final temperature (in degrees celsius) of the metal block? (the specific heat capacity of aluminum, c s, al , is 0.903 j/(g⋅ ∘ c) .) express the temperature in degrees celsius to two significant figures.

Explanation:

At , the heat of vaporization of water is given by:

The water here condenses and gives off heat given by the product between its mass and the heat of vaporization:

The block of aluminum absorbs heat given by the product of its specific heat capacity, mass and the change in temperature:

According to the law of energy conservation, the heat lost is equal to the heat gained:

or:

Rearrange for the final temperature:

We obtain:

Then: