Math Snap

STEP 1

Assumptions1. The energy absorbed by the aluminum fins is2101 J. The initial temperature of the aluminum fins is14.25 °C3. The final temperature of the aluminum fins is23.05 °C4. The specific heat of aluminum is0.897 J/(g°C)
5. The heat absorbed or released by a substance is given by the formula$$q = mc\Delta$$where - q is the heat absorbed or released,
- m is the mass of the substance,
- c is the specific heat of the substance, and - Δ is the change in temperature.

STEP 2

First, we need to calculate the change in temperature. We can do this by subtracting the initial temperature from the final temperature.
$$\Delta =_{final} -_{initial}$$

STEP 3

Now, plug in the given values for the initial and final temperatures to calculate the change in temperature.
$$\Delta =23.05^{\circ}C -14.25^{\circ}C$$

STEP 4

Calculate the change in temperature.
$$\Delta =23.05^{\circ}C -14.25^{\circ}C =8.8^{\circ}C$$

STEP 5

Now that we have the change in temperature, we can rearrange the heat equation to solve for the mass of the aluminum fins. The rearranged equation is$$m = \frac{q}{c\Delta}$$

STEP 6

Plug in the values for the heat absorbed, the specific heat of aluminum, and the change in temperature to calculate the mass.
$$m = \frac{2101 J}{0.897 J/(g°C) \times8.8°C}$$

Calculate the mass of the aluminum fins.
$$m = \frac{2101 J}{0.897 J/(g°C) \times.°C} =268.5 g$$The mass of the aluminum fins that could be heated from14.25 °C to23.05 °C by2101 J of energy is268.5 g.