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 heat must be added to the gear to raise its temperature from 18°C to 53°C?
A)910 J
B)3800 J
C)4000 J
D)4400 J

Question

Quizplus · Accepted Answer

The heat required to raise the temperature of an object is given by $Q = mc\Delta T$, where $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. For a system with multiple materials, the total heat is the sum of the heat required for each material. For iron: $Q_{\text{iron}} = 0.10 \, \text{kg} \times 470 \, \text{J/kg} \cdot \text{K} \times (53 - 18) \, \text{K} = 1645 \, \text{J}$For copper: $Q_{\text{copper}} = 0.16 \, \text{kg} \times 390 \, \text{J/kg} \cdot \text{K} \times (53 - 18) \, \text{K} = 2184 \, \text{J}$Total heat, $Q_{\text{total}} = Q_{\text{iron}} + Q_{\text{copper}} = 1645 \, \text{J} + 2184 \, \text{J} = 3829 \, \text{J}$, which rounds to 3800 J.

A Machine Part Consists of 0