(a) Use the kinetic theory of matter to explain why melting requires energy but there is no change in temperature

Q#1 (Past Exam Paper – June 2007 Paper 4 Q2)

(a) Use the kinetic theory of matter to explain why melting requires energy but there is no change in temperature. [3]

(b) Define specific latent heat of fusion. [2]

(c) A block of ice at 0 °C has a hollow in its top surface, as illustrated in Fig. 2.1.

Fig. 2.1

A mass of 160 g of water at 100 °C is poured into the hollow. The water has specific

heat capacity 4.20 kJ kg^-1 K^-1. Some of the ice melts and the final mass of water in the

hollow is 365 g.

(i) Assuming no heat gain from the atmosphere, calculate a value, in kJ kg^-1, for the

specific latent heat of fusion of ice. [3]

(ii) In practice, heat is gained from the atmosphere during the experiment. This means

that your answer to (i) is not the correct value for the specific latent heat.

State and explain whether your value in (i) is greater or smaller than the correct

value. [2]

Solution:

(a)

During melting, bonds between the molecules are broken/weakened. The kinetic energy does not changed as there is no change in temperature. However, this potential energy of the molecules increases. So, energy is required.

(b)

Specific latent heat of fusion is defined as heat required to convert unit mass of a solid to liquid without any change in temperature (at the normal melting point).

(c)

(i)

{Heat lost by the 160 g of water is given by H = mcΔθ}

thermal energy lost by water  = 0.16 × 4.2 x 100

= 67.2 kJ        

{This heat lost by the hot water is gained by the amount of ice melted.

Amount of (liquid) poured = 160 g

Final mass of water in hollow (= water poured + ice melted) = 365 g

Mass of ice melted = 365 – 160 = 205 g

Heat energy gained by ice when melting is given by H = mL_f}

67.2 = 0.205 × L      

L = 328 kJ kg^-1              

(ii)

The energy gained by the ice would be more than calculated as it also obtains energy from the atmosphere. This causes the calculated value of the specific latent heat to be lower than the accepted value.