Suppose 560.0 J of heat is added to a 111-g piece of aluminum at 23.0° C. What is the final temperature of the aluminum?
To find the final temperature of the aluminum, we can use the equation for heat transfer:
Q = mcΔT
Where:
Q is the amount of heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
In this case, we are given the amount of heat transferred (Q = 560.0 J), the mass of the aluminum (m = 111 g), and the initial temperature of the aluminum (T1 = 23.0°C). We need to find the final temperature (T2).
First, let's convert the mass from grams to kilograms:
m = 111 g = 0.111 kg
The specific heat capacity of aluminum is approximately 0.897 J/(g°C), so we can plug in the known values into the equation and solve for ΔT:
Q = mcΔT
560.0 J = (0.111 kg) * (0.897 J/(g°C)) * ΔT
To solve for ΔT, we can rearrange the equation:
ΔT = Q / (mc)
Now, substitute the values:
ΔT = 560.0 J / (0.111 kg * 0.897 J/(g°C))
Calculating this expression gives us the change in temperature, ΔT.
Finally, to find the final temperature, T2, we add ΔT to the initial temperature:
T2 = T1 + ΔT
Substitute the values of T1 and ΔT into the equation, and calculate to find the final temperature, T2.
To find the final temperature of the aluminum, we can use the equation:
q = m * c * ΔT
where:
q is the heat energy transferred,
m is the mass of the substance (in this case, the aluminum),
c is the specific heat capacity of the substance,
ΔT is the change in temperature.
Let's plug in the known values:
q = 560.0 J
m = 111 g = 0.111 kg (convert grams to kilograms)
c = specific heat capacity of aluminum = 0.903 J/g°C (given value)
ΔT = final temperature - initial temperature
Since we are trying to find the final temperature, we'll rearrange the equation:
ΔT = q / (m * c)
Now we can solve for ΔT:
ΔT = 560.0 J / (0.111 kg * 0.903 J/g°C)
ΔT = 560.0 J / (0.100233 kg * 0.903 J/g°C)
ΔT ≈ 6.187 °C
We can now find the final temperature by adding the change in temperature to the initial temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 23.0 °C + 6.187 °C
Final temperature ≈ 29.187 °C
Therefore, the final temperature of the aluminum is approximately 29.187 °C.