Question

a 6.02 kg piece of copper metal is heated from 20.5 °c to 308.3 °c. calculate the heat absorbed (in kj) by the metal. be sure your answer has the correct number of significant digits. note: reference the phase change properties of pure substances table for additional information.

Explanation:

Step1: Recall the formula for heat absorption

The formula for heat absorbed (\(q\)) by a substance is \(q = mc\Delta T\), where \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the change in temperature. For copper, the specific heat capacity \(c\) is \(0.385\ \text{J/g}^\circ\text{C}\) (from standard phase - change properties tables). First, convert the mass from kilograms to grams: \(m = 6.02\ \text{kg}\times1000\ \text{g/kg}=6020\ \text{g}\).

Step2: Calculate the change in temperature

The initial temperature \(T_i = 20.5^\circ\text{C}\) and the final temperature \(T_f = 308.3^\circ\text{C}\). So, \(\Delta T=T_f - T_i=308.3^\circ\text{C}- 20.5^\circ\text{C}=287.8^\circ\text{C}\).

Step3: Calculate the heat absorbed in joules

Using the formula \(q = mc\Delta T\), substitute \(m = 6020\ \text{g}\), \(c = 0.385\ \text{J/g}^\circ\text{C}\), and \(\Delta T = 287.8^\circ\text{C}\):

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Step4: Convert joules to kilojoules

Since \(1\ \text{kJ}=1000\ \text{J}\), divide the heat in joules by 1000: \(q=\frac{667034.06\ \text{J}}{1000}=667.03406\ \text{kJ}\). Now, consider significant digits. The mass \(6.02\ \text{kg}\) has 3 significant digits, the temperature values have 3 (20.5) and 4 (308.3) significant digits, and the specific heat has 3 significant digits. The least number of significant digits in the given values is 3. So, we round the answer to 3 significant digits.

Answer:

\(667\ \text{kJ}\) (or \(6.67\times 10^{2}\ \text{kJ}\))