Question

a 5.02 kg piece of copper metal is heated from 18.5 °c to 312.3 °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 heat formula

The formula for heat absorbed \( q \) is \( q = mc\Delta T \), where \( m \) is mass, \( c \) is specific heat capacity, and \( \Delta T \) is the change in temperature. For copper, the specific heat capacity \( c = 0.385 \, \text{J/g}^\circ\text{C} \) (or \( 385 \, \text{J/kg}^\circ\text{C} \)). First, convert mass to grams: \( m = 5.02 \, \text{kg} = 5020 \, \text{g} \).

Step2: Calculate temperature change

\( \Delta T = T_2 - T_1 = 312.3^\circ\text{C} - 18.5^\circ\text{C} = 293.8^\circ\text{C} \).

Step3: Calculate heat in joules

Using \( q = mc\Delta T \), substitute values: \( q = 5020 \, \text{g} \times 0.385 \, \text{J/g}^\circ\text{C} \times 293.8^\circ\text{C} \). First, calculate \( 5020 \times 0.385 = 1932.7 \), then \( 1932.7 \times 293.8 \approx 567,927.26 \, \text{J} \).

Step4: Convert to kilojoules

Divide by 1000: \( q = \frac{567927.26}{1000} \approx 568 \, \text{kJ} \) (considering significant digits: 5.02 has 3, 0.385 has 3, 293.8 has 4; result should have 3 significant digits).

Answer:

\boxed{568}