I am in need of help about this specific heat question.

A 100.0g sample of aluminum released 1680 calories when cooled from 100.0 degrees C ti 20.0 degrees C. What is the specific heat of the metal?

I tried setting it up:

1680 cal
________________________
100.0 (100.0 *C- 20.0 *C

i don't believe i set it up correctly.

thank you for your help!!

YOu did set up correctly. Units you used are calories/g-C

That looks ok to me.

I would have done it this way.
q = maxx x sp.H. x (Tfinal-Tinitial)
-1680 = 100 * sp.H.*(20-100)
which gives a negative numerator and a negative denominator BUT the numbers are the same and the - divided by a - is a +. I think 0.21 cal/g is the correct answer.

To solve for the specific heat of aluminum, you can use the formula:

Heat transfer (Q) = mass (m) * specific heat (C) * temperature change (ΔT)

In this case, the mass of the aluminum (m) is given as 100.0 g. The temperature change (ΔT) is the difference between the final temperature (20.0 degrees C) and the initial temperature (100.0 degrees C). In this case, the temperature change is (20.0 - 100.0) = -80.0 degrees C.

The heat transfer (Q) is given as 1680 calories.

Now, by rearranging the equation, you can solve for the specific heat (C):

C = Q / (m * ΔT)

Substituting the given values:

C = 1680 cal / (100.0 g * -80.0 degrees C)

Calculating this gives:

C = -0.21 cal/(g * °C)

Since specific heat is a positive quantity, the negative sign can be ignored, and the specific heat of aluminum is approximately 0.21 cal/(g * °C).