Question

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 2300. J of energy heat from 13.43 ∘C to 22.62 ᵒC ? Aluminum has a specific heat of 0.897 (J/g)⋅ᵒC.

Answer 1

To determine the mass of aluminium that can be heated using 2300 J of energy, the heat equation Q = mcΔT is used. The result is that 279.09 grams of aluminium could be heated from 13.43 °C to 22.62 °C with that amount of energy.

Step-by-step explanation:

To find the mass of aluminium that could be heated from 13.43 °C to 22.62 °C using 2300 J of energy, we use the heat equation Q = mcΔT, where Q is the heat energy transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

Rearranging the equation to solve for mass (m), we get m = Q / (cΔT). Given the specific heat of aluminium (c) as 0.897 J/g°C, we can calculate the change in temperature (ΔT) which is 22.62 °C - 13.43 °C = 9.19 °C.

Substituting the known values into the rearranged equation, the mass of aluminium is m = 2300 J / (0.897 J/g°C × 9.19 °C) = 2300 / (0.897 × 9.19) = 2300 / 8.24163 = 279.09 g.

Therefore, 279.09 grams of aluminium could be heated using 2300 J of energy.