A machine part consists of 0.10 kg of iron (of specific heat 470 J/kg ∙ K )and 0.16 kg of copper (of specific heat 390 J/kg ∙ K).How much thermal energy must be added to the gear to raise its temperature from 18°C to 53°C?

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Quizplus · Accepted Answer

The thermal energy ($Q$) required to raise the temperature of an object can be calculated using the formula $Q = mc\Delta T$, where $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. For a system consisting of multiple materials, the total energy required is the sum of the energy required for each material. For iron: $Q_{\text{iron}} = 0.10 \, \text{kg} \times 470 \, \text{J/kg} \cdot \text{K} \times (53 - 18) \, \text{K} = 0.10 \times 470 \times 35 = 1645 \, \text{J}$For copper: $Q_{\text{copper}} = 0.16 \, \text{kg} \times 390 \, \text{J/kg} \cdot \text{K} \times (53 - 18) \, \text{K} = 0.16 \times 390 \times 35 = 2184 \, \text{J}$Total energy required: $Q_{\text{total}} = Q_{\text{iron}} + Q_{\text{copper}} = 1645 \, \text{J} + 2184 \, \text{J} = 3829 \, \text{J}$Rounding to the nearest hundred gives approximately 3800 J.

A Machine Part Consists of 0