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 2138 J of energy heat from 14.83 ∘C to 23.31 ∘C?

Answer 1

Using the heat transfer equation Q = mcΔT and the specific heat capacity of aluminum, the mass of aluminum that can be heated from 14.83°C to 23.31°C with 2138 J of energy is 281 grams.

Step-by-step explanation:

To calculate the mass of aluminum that a given amount of energy can heat from one temperature to another, we can use the heat transfer equation Q = mcΔT, where Q is the heat energy transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

Given the specific heat capacity of aluminum (900 J/kg°C) and an energy transfer of 2138 J, we can rearrange the equation to solve for m:

m = Q / (cΔT)

The change in temperature, ΔT, is the final temperature minus the initial temperature, which is 23.31°C - 14.83°C = 8.48°C. Inserting these values into the equation, we get:

m = 2138 J / (900 J/kg°C × 8.48°C)

Solving for m gives us the mass in kilograms, which can then be converted to grams.

The mass of aluminum that can be heated is therefore:

m = 2138 J / (900 J/kg°C × 8.48°C) = 0.281 kg = 281 g

Answer 2

The correct answer is 281.39 grams.

Step-by-step 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.