QuestionMay 7, 2025

Calculate the energy required to heat 403.0 g of water from 31.9^circ C to 41.3^circ C Assume the specific heat capacity of water under these conditions is 4.18Jcdot g^-1cdot K^-1 . Be sure your answer has the correct number of significant digits. square

Calculate the energy required to heat 403.0 g of water from 31.9^circ C to 41.3^circ C Assume the specific heat capacity of water under these conditions is 4.18Jcdot g^-1cdot K^-1 . Be sure your answer has the correct number of significant digits. square
Calculate the energy required to heat 403.0 g of water from 31.9^circ C to 41.3^circ C Assume the specific heat capacity of water under these conditions is 4.18Jcdot g^-1cdot K^-1 . Be sure your answer has the correct number of significant digits. square

Solution
4.1(248 votes)

Answer

15800 \, J Explanation 1. Calculate the temperature change \Delta T = 41.3^{\circ}C - 31.9^{\circ}C = 9.4^{\circ}C 2. Apply the formula for heat energy Use **q = m \cdot c \cdot \Delta T**, where m = 403.0 \, g, c = 4.18 \, J \cdot g^{-1} \cdot K^{-1}, and \Delta T = 9.4 \, K. 3. Perform the calculation q = 403.0 \, g \times 4.18 \, J \cdot g^{-1} \cdot K^{-1} \times 9.4 \, K = 15830.964 \, J 4. Round to correct significant figures The least number of significant figures in the given data is 3 (from 9.4), so round 15830.964 \, J to 15800 \, J.

Explanation

1. Calculate the temperature change<br /> $\Delta T = 41.3^{\circ}C - 31.9^{\circ}C = 9.4^{\circ}C$<br /><br />2. Apply the formula for heat energy<br /> Use **$q = m \cdot c \cdot \Delta T$**, where $m = 403.0 \, g$, $c = 4.18 \, J \cdot g^{-1} \cdot K^{-1}$, and $\Delta T = 9.4 \, K$.<br /><br />3. Perform the calculation<br /> $q = 403.0 \, g \times 4.18 \, J \cdot g^{-1} \cdot K^{-1} \times 9.4 \, K = 15830.964 \, J$<br /><br />4. Round to correct significant figures<br /> The least number of significant figures in the given data is 3 (from $9.4$), so round $15830.964 \, J$ to $15800 \, J$.
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