When 24.0 cal of heat is added to 18.5 g of aluminum at 19.0 ∘C, what is the final temperature of the aluminum?

To find the final temperature of the aluminum, we can use the formula for heat transfer:

Q = mcΔT

where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

In this case, we know Q (24.0 cal), m (18.5 g), c (the specific heat capacity of aluminum is 0.897 J/g⋅°C), and the initial temperature (19.0 ∘C). We need to find the final temperature.

First, let's convert the mass of aluminum to grams:

m = 18.5 g

Next, let's convert the heat from calories to joules since the specific heat capacity of aluminum is given in joules per gram per degree Celsius:

Q = 24.0 cal * 4.184 J/cal = 100.416 J

Now, we can use the formula to find the change in temperature and then add it to the initial temperature to get the final temperature:

Q = mcΔT

ΔT = Q / (mc)

ΔT = 100.416 J / (18.5 g * 0.897 J/g⋅°C)

ΔT ≈ 6.172 °C

Finally, we can add the change in temperature to the initial temperature:

Final temperature = Initial temperature + ΔT
Final temperature ≈ 19.0 ∘C + 6.172 ∘C
Final temperature ≈ 25.172 ∘C

Therefore, the final temperature of the aluminum is approximately 25.172 ∘C.

q = mass Al x specific heat Al x (Tfinal-Tinitial)