Suppose that 0.50 g of water at 25 ∘c condenses on the surface of a 51-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 ∘c) of the metal block? (the specific heat capacity of aluminum is 0.903 j/g∘c and the heat of vaporization of water at 25 ∘c is 44.0 kj/mol.)

Moles water = 0.50 g / 18.02 g/mol=0.0277

heat lost by water = 0.0277 mol x 44.0 kJ/mol=1.22 kJ => 1220 J 
heat gained by aluminum = 1220 J 

1220 = 51 x 0.903 ( T - 25) = 46.05 T - 1151
1220 + 1151 = 46.05T 

46.05T = 2371
T = 51.48 °C (51 °C at two significant figures)

The final temperature of the metal block is about 51.5°C

Let's recall the Specific Heat Capacity formula as follows:

where :

Q = heat energy ( J )

m = mass of object ( kg )

c = specific heat capacity ( J/kg°C )

Δt = change in temperature ( °C )

Let us now tackle the problem!

Given:

mass of water = m = 0.50 g

mass of aluminium = M = 51 g

initial temperature of aluminium = to = 25°C

specific heat capacity of aluminium = c = 0.903 J/g°C

heat of vaporization of water = Lv = 44.0 kJ/mol =44000 J/mol

molar mass of water = 18 g/mol

Asked:

final temperature of aluminium = t = ?

Solution:

We will use Conservation of Energy formula as follows:

Grade: High School

Subject: Mathematics

Chapter: Energy