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.