Question

Determine the latent heat of fusion of mercury using the following calorimeter data: 1 kg of solid mercury (1) at its melting point of -39 \deg C is placed in a 0.62 kg aluminum (2) calorimeter with 0.4 kg of water (3) at 12.8 \deg C, the resulting equilibrium temperature is 5.06 \deg C.

a. Write out in English the process that this system will undergo.

b. Write out all givens using the assignments above (Mercury = 1, Aluminum = 2, and water = 3)

c. Determined the latent heat of fusion for mercury by setting up your simulation statement.

Answer 1

given

specific heat of Hg, c₁ =138 J/kg^oC

specific heat of aluminum, c₂ = 900 J/kg^oC

specific heat of water, c₃ = 4186 J/kg^oC

mass of the solid Hg is m₁ = 1 kg

mass of the aluminum container is m₂ = 0.62 kg

mass of the water is m₃ = 0.4 kg

temperature of Hg is t₁ = - 39^oC

temperature of aluminum + water is t2 = 12.8^oC

resultant temperature, t = 5.06^oC

according to calorimetry

m₁ L +  m₁ c₁ ( t - t₁ ) = m₃ c₃ ( t₂ - t ) +  m₂ c₂ ( t₂ - t )

1 x L + 1 x 138 ( 5.06 + 39 ) = ( 0.4 ) ( 4186 ) ( 12.8 - 5.06 ) + ( 0.620 ) ( 900 ) ( 12.8 - 5.06 )

L + 6.08 x 10³ = 1.3 x 10⁴ + 4.32 x 10³

L = ( 1.3 x 10⁴ + 4.32 x 10³ ) - 6.08 x 10³

L = 1.124 x 10⁴ J/kg

L = 11.24 kJ/kg