Chapter 10, Problem 26A

Interpretation Introduction

Interpretation : The specific heat capacity of the metal in $\text{J}/\text{g}°\text{C}$ is to be calculated.

Concept Introduction : The heat transfer during a reaction is given by,

  $\text{Q}=\text{mc}\Delta \text{T}$

Where,

• $\text{Q}$ represents heat.
• $\text{m}$ represents mass.
• $\text{c}$ represents specific heat.
• $\Delta \text{T}$ represents change in the temperature.

Answer to Problem 26A

The specific heat capacity of the metal in $\text{J}/\text{g}°\text{C}$ is $\text{0}\text{.710}\text{J}/\text{g}°\text{C}$ .

Explanation of Solution

Given information: The given mass is $\text{952}\text{g}$ . The given heat is $\text{7}\text{.24}\text{kJ}$ . The given temperature is $\text{10}\text{.7}°\text{C}$ .

Substitute the given value of mass, heat and temperature in the formula.

  $\begin{array}{c}\text{Q}=\text{mc}\Delta \text{T}\\ 7.24\text{kJ}=952\text{g}\times \text{c}\times 10.7°\text{C}\\ \text{c}=\frac{7.24\text{kJ}}{952\text{g}\times 10.7°\text{C}}\\ =0.000710\text{kJ}/\text{g}°\text{C}\end{array}$

The conversion of $\text{kJ}$ into $\text{J}$ is as follows.

  $1\text{kJ}=1000\text{J}$

Therefore, the conversion of calculated values in $\text{J}$ is as follows.

  $\begin{array}{c}1\text{kJ}=1000\text{J}\\ \text{0}\text{.000710}\text{kJ}=\text{0}\text{.000710}\times 1000\text{J}\\ =\text{0}\text{.710}\text{J}\end{array}$

Conclusion

The specific heat capacity of the metal in $\text{J}/\text{g}°\text{C}$ is $\text{0}\text{.710}\text{J}/\text{g}°\text{C}$ .