Calculate the energy required to heat 567.0mg of aluminum from 12.5°C to 24.0°C. Assume the specific heat capacity of aluminum under these conditions is ·0.903J·g−1K−1 . Be sure your answer has the correct number of significant digits.
Question
Calculate the energy required to heat 567.0mg of aluminum from 12.5°C to 24.0°C. Assume the specific heat capacity of aluminum under these conditions is ·0.903J·g−1K−1 . Be sure your answer has the correct number of significant digits.
Solution
To calculate the energy required to heat a substance, you can use the formula:
q = mcΔT
where:
- q is the heat energy (in Joules)
- m is the mass (in grams)
- c is the specific heat capacity (in J/g·K)
- ΔT is the change in temperature (in Kelvin or Celsius, since the scale is the same)
First, convert the mass from milligrams to grams:
567.0 mg = 0.567 g
The change in temperature, ΔT, is the final temperature minus the initial temperature:
ΔT = 24.0°C - 12.5°C = 11.5°C
Now, plug the values into the formula:
q = (0.567 g) * (0.903 J/g·K) * (11.5 K) = 5.88 J
So, the energy required to heat 567.0 mg of aluminum from 12.5°C to 24.0°C is approximately 5.88 Joules.
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