Chapter 8, Problem 1QAP

Principles of Heat Flow

Titanium is a metal used in jet engines. Its specific heat is 0.523 J/g $\cdot$

°C. If S.SS g of titanium absorb 4.78 J, what is the change in temperature?

Interpretation Introduction

Interpretation:When titanium absorbs 4.78 J of energy, the change in temperature needs to be calculated.

Concept introduction:

Relation between specific heat, mass and change in temperature is as follows:

  $\begin{array}{l}\text{Q=}\text{mCΔT}\\ \text{where,}\\ \text{Q=amount}\text{of}\text{energy(J)}\\ \text{m}\text{=}\text{mass}\text{of}\text{substance}\text{(g)}\\ \text{C=}\text{specific}\text{heat}\text{(J/g}\text{.°C)}\\ \text{ΔT}\text{=}{\text{T}}_{\text{2}}{\text{-T}}_{\text{1}}\text{=}\text{change}\text{in}\text{temperature}\end{array}$

Answer to Problem 1QAP

Change in temperature is 1.55°C.

Explanation of Solution

Mass of titanium, m = 5.88 g

Amount of energy absorbed, Q = 4.78 J

Specific heat of titanium, C = 0.523 J/g.°C

Plugging values to calculate change in temperature as:

  $\begin{array}{l}\text{Q=}\text{mCΔT}\\ \Rightarrow \text{4}\text{.78}\text{ J=}\text{(5}\text{.88 g)×(0}{\text{.523 J/g }}^{\text{o}}\text{C)×(ΔT)}\\ \Rightarrow \text{ΔT}\text{=}\frac{\text{4}\text{.78}}{\text{5}\text{.88×0}\text{.523}}{}^{\text{o}}\text{C}=\text{1}\text{.55°C}\end{array}$

Conclusion

Thus, the change in temperature is 1.55°C.