Calculate the energy required to heat 1.40kg of iron from −5.2°C to 0.9°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 1.40kg of iron from −5.2°C to 0.9°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.
First, we need to convert the mass from kg to g because the specific heat capacity is given in J/g·K.
1.40 kg = 1.40 * 1000 g = 1400 g
Next, we calculate the change in temperature (ΔT).
ΔT = T_final - T_initial = 0.9°C - (-5.2°C) = 6.1°C
Now we can substitute these values into the formula:
Q = (1400 g) * (0.449 J/g·K) * (6.1 K) = 3881.54 J
The number of significant figures should be the same as the number in the question with the least number of significant figures. In this case, the least number of significant figures in the question is 3 (from the value 1.40 kg). Therefore, we should round our answer to 3 significant figures:
Q = 3880 J
So, the energy required to heat 1.40 kg of iron from -5.2°C to 0.9°C is 3880 J.
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