Chapter 15.1, Problem 6PP

Interpretation Introduction

Interpretation:

The final temperature of pure gold is to be calculated when gold absorbs heat.

Concept introduction:

Specific heat is defined as quantity of heat required to raise the temperature of one gram substance by one Kelvin. It is represented by ‘c’.

Answer to Problem 6PP

The final temperature is $500.5°C$.

Explanation of Solution

The quantity of heat required can be calculated by using formula:

$\begin{array}{l}q=mc\Delta T\\ whereqisquantityofheatabsorbed\\ m=givenmass\\ T_1=initialtemperature\\ T_2=finaltemperature\\ \Delta T=riseintemperature\\ cisspecificheat\\ \therefore \Delta T=\frac{q}{mc}\\ or\\ T_2-T_1=\frac{q}{mc}\end{array}$

Given data:

$\begin{array}{l}m=4.50g\\ T_1=25°C\\ q=276J\\ c=0.129J/g-°C\end{array}$

Substituting the values in formula:

$\begin{array}{c}{T}_2-T_1=\frac{q}{mc}\\ T_2-25=\frac{276}{4.50\times 0.129}\\ T_2-25=475.5°C\\ T_2=500.5°C\end{array}$

Conclusion

Thus, the final temperature of gold is $500.5°C$.