Question

The amount of heat required to reach the outer skin of aluminium to its boiling point is

• A. 129.7 J
• B. 140.7 J
• C. 196.4 J
• D. 554.7 J

Answer 1

Answer: (A)

129.7 J

Answer 2

The heat required to raise the temperature of a substance is given by the formula $Q = mc\Delta T$. \begin{itemize} \item Change in temperature ($\Delta T$): $2500^\circ C - (-50^\circ C) = 2550^\circ C$. \item Volume of aluminium heated: The laser spot has a radius of $0.5 \text{ mm} = 0.05 \text{ cm}$. The area is $A = \pi r^2 = \pi (0.05 \text{ cm})^2 = 0.0025\pi \text{ cm}^2$. The volume is $V = A \times \text{thickness} = (0.0025\pi \text{ cm}^2) \times (3 \text{ cm}) = 0.0075\pi \text{ cm}^3$. \item Mass of aluminium ($m$): $m = \text{density} \times V = (2.4 \text{ g/cm}^3) \times (0.0075\pi \text{ cm}^3) = 0.018\pi \text{ g}$. \item Heat required ($Q$): $Q = mc\Delta T = (0.018\pi \text{ g}) \times (0.9 \text{ J/g}^\circ C) \times (2550^\circ C) = 41.31\pi \text{ J}$. Using $\pi \approx 3.14159$, $Q \approx 41.31 \times 3.14159 \text{ J} \approx 129.78 \text{ J}$. \end{itemize}