Chapter 9, Problem 9.14P

Interpretation Introduction

Interpretation:

The heats of fusion should be converted from units of J/cm³ to kJ/kg.

Concept introduction:

The heat of fusion is a change in its enthalpy which results from the heat in the form of energy to change the certain state of a substance from solid to liquid.

The heat of fusion is also called a latent heat of fusion.

The heat of fusion is endothermic process and change in enthalpy is positive.

Answer to Problem 9.14P

Conversion of Ga from J/cm³ to kJ/kg is 82.656.

Conversion of Bi from J/cm³ to kJ/kg is 55.363.

Conversion of Pb from J/cm³ to kJ/kg is 20.862.

Conversion of Ag from J/cm³ to kJ/kg is 92.

Conversion of Cu from J/cm³ to kJ/kg is 92.

Conversion of Ni from J/cm³ to kJ/kg is 309.6.

Conversion of Fe from J/cm³ to kJ/kg is 220.11.

Explanation of Solution

Given Information:

Material	Freezing Temp (Tm)Degree Celsius	The heat of fusion ($\Delta H_f$)J/cm3	Solid-liquid interfacial energy (${\sigma }_{SL}$)J/cm3	Typical under cooling for homogenous nucleation ($\Delta T$) Degree Celsius
Ga	30	488	$56\times {10}^{-7}$	76
Bi	271	543	$54\times {10}^{-7}$	90
Pb	327	237	$33\times {10}^{-7}$	80
Ag	962	965	$126\times {10}^{-7}$	250
Cu	1085	1628	$177\times {10}^{-7}$	236
Ni	1453	2756	$255\times {10}^{-7}$	480
Fe	1538	1737	$204\times {10}^{-7}$	420
NaCl	801			169
CsCl	645			152
H2O	0			40

The equation for the heat of fusion is as follows:

  $\Delta H_f=\frac{(\Delta H_f)}{\varsigma }$ ................................. (1)

Substitute value of ${(\Delta H_f)}_{G_a}$ from table and ${\varsigma }_{G_a}$ equal to 5.904 g/cm³ in equation (1);

  $\Delta H_f=\frac{488}{5.904}=\frac{{\text{488J/cm}}^{\text{3}}\text{×}\frac{{\text{10}}^{\text{-3}}{\text{kJ/cm}}^{\text{3}}}{{\text{J/cm}}^{\text{3}}}}{\text{5}\text{.904×}\frac{{\text{10}}^{\text{-3}}{\text{kg/cm}}^{\text{3}}}{{\text{g/cm}}^{\text{3}}}}=82.65\text{6}\text{kJ/kg}$

Substitute value of ${(\Delta H_f)}_{Bi}$ from table and ${\varsigma }_{Bi}$ equal to 9.808 g/cm³ in equation (1);

  $(\Delta H_f)=\frac{543}{9.808}=\frac{{\text{543J/cm}}^{\text{3}}\text{×}\frac{{\text{10}}^{\text{-3}}{\text{kJ/cm}}^{\text{3}}}{{\text{J/cm}}^{\text{3}}}}{\text{9}{\text{.808×10}}^{\text{-3}}\frac{{\text{kg/cm}}^{\text{3}}}{{\text{g/cm}}^{\text{3}}}}=55.3\text{63kJ/kg}$

Substitute value of ${(\Delta H_f)}_{Pb}$ from table and ${\varsigma }_{Pb}$ equal to 11.36 g/cm³ in equation (1);

  $(\Delta H_f)=\frac{237}{11.36}=\frac{{\text{237J/cm}}^{\text{3}}\text{×}\frac{{\text{10}}^{\text{-3}}{\text{kJ/cm}}^{\text{3}}}{{\text{J/cm}}^{\text{3}}}}{\text{11}{\text{.36×10}}^{\text{-3}}\frac{{\text{kg/cm}}^{\text{3}}}{{\text{g/cm}}^{\text{3}}}}=20.86\text{2 kJ/kg}$

Substitute value of ${(\Delta H_f)}_{Ag}$ from table and ${\varsigma }_{Ag}$ equal to 10.49 g/cm³ in equation (1);

  $(\Delta H_f)=\frac{965}{10.49}=\frac{{\text{965 J/cm}}^{\text{3}}\text{×}\frac{{\text{10}}^{\text{-3}}{\text{ kJ/cm}}^{\text{3}}}{{\text{J/cm}}^{\text{3}}}}{\text{10}{\text{.49×10}}^{\text{-3}}\frac{{\text{kg/cm}}^{\text{3}}}{{\text{g/cm}}^{\text{3}}}}=\text{92 kJ/kg}$

Substitute value of ${(\Delta H_f)}_{Cu}$ from table and ${\varsigma }_{Cu}$ equal to 8.93 g/cm³ in equation (1);

  $(\Delta H_f)=\frac{1628}{8.93}=\frac{1628J/c{m}^3\times \frac{10^{-3}\text{k}J/c{m}^3}{J/c{m}^3}}{8.93\times 10^{-3}\frac{kg/c{m}^3}{g/c{m}^3}}=92\text{kJ/kg}$

Substitute value of ${(\Delta H_f)}_{Ni}$ from table and ${\varsigma }_{Ni}$ equal to 8.902 g/cm³ in equation (1);

  $(\Delta H_f)=\frac{2756}{8.902}=\frac{{\text{2756 J/cm}}^{\text{3}}\text{×}\frac{{\text{10}}^{\text{-3}}{\text{kJ/cm}}^{\text{3}}}{{\text{J/cm}}^{\text{3}}}}{\text{8}{\text{.902×10}}^{\text{-3}}\frac{{\text{kg/cm}}^{\text{3}}}{{\text{g/cm}}^{\text{3}}}}=309.\text{6kJ/kg}$

Substitute value of ${(\Delta H_f)}_{Fe}$ from table and ${\varsigma }_{Fe}$ equal to 7.87 g/cm³ in equation (1);

  $(\Delta H_f)=\frac{1737}{7.87}=\frac{{\text{1737J/cm}}^{\text{3}}\text{×}\frac{{\text{10}}^{\text{-3}}{\text{kJ/cm}}^{\text{3}}}{{\text{J/cm}}^{\text{3}}}}{\text{7}{\text{.87×10}}^{\text{-3}}\frac{{\text{kg/cm}}^{\text{3}}}{{\text{g/cm}}^{\text{3}}}}=220.71\text{kJ/kg}$

All the values of densities of the materials from the density of materials from appendix A.

Conclusion

Thus, using the equation of heat of fusion and values of densities the heat of the materials can be converted from J/cm³ to kJ/kg.