TE-2 At 175 'C, a brass plate completely fills a frame which has dimensions 2.38 m by 1.67 m. Ignoring the thermal expansion of the frame, to what temperature would the brass plate need to be cooled so that it only fills 99.5% area of the frame? 2.38 m brass plate in the frame at 175 °C 1.67 for brass, a = 19.0x10-6 °C-1 m

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Chapter1: Units, Trigonometry. And Vectors
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**Problem: Thermal Expansion of Brass Plate**

**Scenario:** At 175°C, a brass plate completely fills a frame with dimensions 2.38 m by 1.67 m. Ignoring the thermal expansion of the frame, to what temperature would the brass plate need to be cooled so that it only fills 99.5% of the area of the frame?

**Given Data:**

- Dimensions of frame:
  - Length: 2.38 m
  - Width: 1.67 m

- Thermal expansion coefficient for brass, \( \alpha = 19.0 \times 10^{-6} \, \text{°C}^{-1} \)

**Visual Explanation:**

The diagram accompanying the text shows a rectangular frame with dimensions labeled:
- **Length:** 2.38 m (horizontal dimension)
- **Width:** 1.67 m (vertical dimension)

The brass plate is represented by a yellow rectangle completely filling the black-bordered frame. The problem asks for the temperature change required for the brass plate to fill 99.5% of the frame’s area.

This problem involves calculating the reduction in temperature needed for the desired change in the plate's area, taking into account the linear expansion properties of brass.
Transcribed Image Text:**Problem: Thermal Expansion of Brass Plate** **Scenario:** At 175°C, a brass plate completely fills a frame with dimensions 2.38 m by 1.67 m. Ignoring the thermal expansion of the frame, to what temperature would the brass plate need to be cooled so that it only fills 99.5% of the area of the frame? **Given Data:** - Dimensions of frame: - Length: 2.38 m - Width: 1.67 m - Thermal expansion coefficient for brass, \( \alpha = 19.0 \times 10^{-6} \, \text{°C}^{-1} \) **Visual Explanation:** The diagram accompanying the text shows a rectangular frame with dimensions labeled: - **Length:** 2.38 m (horizontal dimension) - **Width:** 1.67 m (vertical dimension) The brass plate is represented by a yellow rectangle completely filling the black-bordered frame. The problem asks for the temperature change required for the brass plate to fill 99.5% of the frame’s area. This problem involves calculating the reduction in temperature needed for the desired change in the plate's area, taking into account the linear expansion properties of brass.
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