Explanation:
We have an aluminum sample that has a mass of 91 g. Its initial temperature is 22 °C and we apply to it 874 J. We have to find the final temperature of the aluminum sample.
To find the final temperature we can use the following formula:
Q = m * C * ΔT
Where Q is the amount of heat that the sample gained or lost, m is the mass of the sample, C is the specific heat and ΔT is the temperature change.
We already know some of these values.
Q = 874 J
m = 91 g
C = 0.90 J/g°C
ΔT = Tfinal - Tinitial
ΔT = Tfinal - 22 °C
Now we can replace these values in the previous formula and solve it for Tfinal to get the answer to our problem.
Q = m * C * ΔT
874 J = 91 g * 0.90 J/(g°C) * (Tfinal - 22 °C)
874 J/(91 g * 0.90 J/(g°C)) = (Tfinal - 22 °C)
Tfinal = 10.7 °C + 22 °C
Tfinal = 32.7 °C = 33 °C
Answer: The final temperature is 33 °C.
