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

b) returns freshwater to the earth.

c) returns freshwater to the earth.c) occurs after condensation.

d) returns freshwater to the earth.c) occurs after condensation.d) roughly equal to the amount of evaporation.

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