Answer:
Approximately [tex]330\; {\rm J}[/tex] ([tex]3.30 \times 10^{2}\; {\rm J}[/tex], rounded to [tex]2[/tex] significant figures.)
Explanation:
Consider a material with a specific heat capacity of [tex]c[/tex]. Increasing the temperature of [tex]m[/tex] (mass) of this material by [tex]\Delta T[/tex] would require [tex]Q = c\, m\, \Delta T[/tex] of energy.
In this question:
- The specific heat capacity of aluminum is: [tex]c = 0.89\; {\rm J \cdot g^{-1} \cdot (^{\circ} C)^{-1}}[/tex].
- The mass of the aluminum to heat up is: [tex]m = 12\; {\rm g}[/tex].
The question asked for a temperature increase of [tex]\Delta T = (52 - 21) \; {\rm ^{\circ} C} = 31\; {\rm ^{\circ} C}[/tex]. Apply the equation [tex]Q = c\, m\, \Delta T[/tex] to find the amount of energy [tex]Q[/tex] required for this temperature change:
[tex]\begin{aligned} Q &= c\, m\, \Delta T \\ &= 0.89\; {\rm J \cdot g^{-1} \cdot (^{\circ} C)^{-1}} \times 12\; {\rm g} \times 31 \; {\rm {^{\circ} C} \\ &\approx 3.3 \times 10^{2}\; {\rm J}\end{aligned}[/tex].
