The heat equation, as given in the introduction, can also be rearranged to calculate the mass or temperature change for a substance. Follow the same steps used to calculate the quantity of heat gained or lost, but when you solve the equation, the term for mass or temperature change must be isolated on one side of the equation. What mass, in grams, of aluminum fins could 2138 J of energy heat from 14.83 ∘C to 23.31 ∘C?

The correct answer is 281.39 grams.

Explanation:

To arrive at this answer you must first keep in mind the basic equation:

Q = m*Cp * ΔT

Now, in order to calculate the necessary aluminum mass that absorbs 2138 J when passing from 14.83 to 23.31 ° C you must "clear" m of the previous equation.

This means, leave only the mass on one side of the equation, and "pass" Cp and ΔT to the other side dividing Q. This would look like this:

m = Q / (Cp*ΔT)

Then, you need the value of specific heat of aluminum in the correct units, that is J / g ° C, the approximate value is 0.896.

ΔT is calculated by doing the mathematical operation:

23.31 °C - 14.83 °C = 8.48 °C

Finally, the values of: Q (data provided in joules), Cp (J / g ° C) and ΔT (calculated in ° C) are replaced in the last equation and the mass (in grams) is calculated resulting in 281.39 grams.