Chapter 10, Problem 27A

Interpretation Introduction

Interpretation: The substance for which the temperature will increase the most needs to be determined, if 75.0 g of copper, silver and gold are taken at 24.0°C as initial temperature and 2.00 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 27A

The solid gold has least specific heat capacity so it must show highest temperature change.

  $\text{ΔT}=\text{ 205 }°\text{C}$

Explanation of Solution

Given information:

Mass of copper, silver and gold = 75.0 g

Initial temperature = 24.0°C

Heat supplied = 2.00 kJ

Mass of copper, silver and gold = 75.0 g

Initial temperature = 24.0°C

Heat supplied = 2.00 kJ

Calculation:

Calculate temperature change for each sample with the help of their specific heat capacity:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{ΔT=}\frac{\text{q}}{\text{m× C }}\end{array}$

Substitute the values to calculate temperature change for copper:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{2}\text{.00}\times {\text{10}}^{\text{3}}\text{ J = 75}\text{.0 g × 0}\text{.385 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{2}\text{.00}\times {\text{10}}^{\text{3}}\text{ J }}{\text{75}\text{.0 g × 0}\text{.385 J/g}°\text{C}}\text{ = 69}\text{.3 }°\text{C}\end{array}$

Substitute the values to calculate temperature change for silver:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{2}\text{.00}\times {\text{10}}^{\text{3}}\text{ J = 75}\text{.0 g × 0}\text{.24 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{2}\text{.00}\times {\text{10}}^{\text{3}}\text{ J }}{\text{75}\text{.0 g × 0}\text{.24 J/g}°\text{C}}\text{ = 111 }°\text{C}\end{array}$

Substitute the values to calculate temperature change for gold:

  $\begin{array}{l}\text{q = m× C × ΔT}\\ \text{2}\text{.00}\times {\text{10}}^{\text{3}}\text{ J = 75}\text{.0 g × 0}\text{.13 J/g}°\text{C × ΔT}\\ \text{ΔT}=\frac{\text{2}\text{.00}\times {\text{10}}^{\text{3}}\text{ J }}{\text{75}\text{.0 g × 0}\text{.13 J/g}°\text{C}}\text{ = 205 }°\text{C}\end{array}$

Thus the highest temperature change is for solid gold.

Conclusion

Thus, $\text{ΔT}=\text{205 }°\text{C}$ for gold or it has higher temperature change.