Chapter 10, Problem 50A

Interpretation Introduction

Interpretation: The mass of silver sample needs to be determined if $1.25\text{KJ}$ of energy is required for heating the sample of pure silver from $12.0°\text{C}$ to $15.2°\text{C}$ .

Concept introduction: Specific heat of capacity can be defined as the amount of heat added to a substance to raise the temperature by one degree.

Answer to Problem 50A

The mass of silver sample will be $1.63\times {10}^3\text{g}$ .

Explanation of Solution

The specific heat capacity of silver is $0.24\text{J/g°C}$ .

The amount of heat required for heating the silver sample from $12.0°\text{C}$ to $15.2°\text{C}$ is $1.25\text{KJ}$ .

Now, the mass of the silver sample can be calculated as:

  $\begin{array}{c}Q=s\times m\times \Delta T\\ 1.25\text{KJ}=0.24\text{J/g°C}\times m\times \left(15.2-12.0\right)\text{°C}\\ m=\frac{1.25KJ}{0.24\text{J/g°C}\times 3.2\text{°C}}\times \frac{\text{1000}\text{J}}{\text{1}\text{KJ}}\\ =1.63\times {10}^3\text{g}\end{array}$

Hence, the mass of silver sample will be $1.63\times {10}^3\text{g}$ .

Conclusion

The equation for the calculation of mass is as follows:

  $Q=s\times m\times \Delta T$

Where, Q is the amount of heat, m is the mass of substance, s is the specific heat capacity and $\Delta T$ is the temperature change.