Calculate the energy required to heat 328.0g of iron from −5.1°C to 2.0°C. Assume the specific heat capacity of iron under these conditions is ·0.449J·g−1K−1 . Be sure your answer has the correct number of significant digits.
Question
Calculate the energy required to heat 328.0g of iron from −5.1°C to 2.0°C. Assume the specific heat capacity of iron under these conditions is ·0.449J·g−1K−1 . Be sure your answer has the correct number of significant digits.
Solution
To calculate the energy required to heat the iron, we can use the formula for heat transfer:
q = mcΔT
where:
- q is the heat energy,
- m is the mass,
- c is the specific heat capacity, and
- ΔT is the change in temperature.
Given:
- m = 328.0 g,
- c = 0.449 J/g·K, and
- ΔT = 2.0°C - (-5.1°C) = 7.1°C = 7.1 K (since a change of 1°C is equivalent to a change of 1 K).
Substituting these values into the formula gives:
q = (328.0 g) * (0.449 J/g·K) * (7.1 K) = 1036.892 J
However, we need to consider significant figures. The given values have at most four significant figures, so our final answer should also have four significant figures. Therefore, the energy required to heat 328.0 g of iron from -5.1°C to 2.0°C is approximately 1037 J.
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