Chapter 10, Problem 58A

Interpretation Introduction

Interpretation: The temperature raised for10.0 g of each sample needs to be determined, if 1.00 kJ of heat is applied.

Concept Introduction: Specific heat capacity can be defined as the heat in joules that is required to raise the temperature of 1 g of substance by 1°C. The relation between specific heat capacity and heat required is shown below:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{q = heat }\\ \text{m = mass }\\ \text{C = specific heat capacity }\\ \text{ΔT= temperature change}\end{array}$

Answer to Problem 58A

Substance	Temperature change (°C)
Water	23.9
Ice	49.3
Steam	50
Aluminium	112
Iron	222
Mercury	714
Carbon	141
Silver	417
Gold	769
Copper	260

Explanation of Solution

Heat = 1.00 kJ = 1000 J

Mass = 10.0 g

• Specific heat capacity for water = 4.184 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 4}\text{.184 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 4}\text{.184 J/g}°\text{C}}\text{ =23}\text{.9}°\text{C}\end{array}$

• Specific heat capacity for ice = 2.03 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 2}\text{.03 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 2}\text{.03 J/g}°\text{C}}\text{ =49}\text{.3 }°\text{C}\end{array}$

• Specific heat capacity for steam = 2 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 2 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 2 J/g}°\text{C}}\text{ = 50 }°\text{C}\end{array}$

• Specific heat capacity for Aluminium = 0.89 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 0}\text{.89 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 0}\text{.89 J/g}°\text{C}}\text{ = 112 }°\text{C}\end{array}$

• Specific heat capacity for iron = 0.45 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 0}\text{.45 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 0}\text{.45 J/g}°\text{C}}\text{ = 222 }°\text{C}\end{array}$

• Specific heat capacity for liquid mercury = 0.14 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 0}\text{.14 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 0}\text{.14 J/g}°\text{C}}\text{ = 714 }°\text{C}\end{array}$

• Specific heat capacity for carbon = 0.71 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 0}\text{.71 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 0}\text{.71 J/g}°\text{C}}\text{ = 141 }°\text{C}\end{array}$

• Specific heat capacity for Silver = 0.24 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 0}\text{.24 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 0}\text{.24 J/g}°\text{C}}\text{ = 417 }°\text{C}\end{array}$

• Specific heat capacity for Gold = 0.13 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 0}\text{.13 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 0}\text{.13 J/g}°\text{C}}\text{ = 769 }°\text{C}\end{array}$

• Specific heat capacity for copper = 0.385 J/g°C
Substitute the values to calculate temperature change:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{1000 J = 10}\text{.0 g × 0}\text{.385 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{1000 J}}{\text{10}\text{.0 g × 0}\text{.385 J/g}°\text{C}}\text{ = 260 }°\text{C}\end{array}$

Conclusion

Thus,

Substance	Temperature change (°C)
Water	23.9
Ice	49.3
Steam	50
Aluminium	112
Iron	222
Mercury	714
Carbon	141
Silver	417
Gold	769
Copper	260