### Thermal Expansion Problem#### Problem Statement:At a temperature of 9°C, a 3-mm gap exists between two polymer bars and a rigid support, as shown in the figure. Bars (1) and (2) have coefficients of thermal expansion of \(\alpha_1 = 139 \times 10^{-6} \, \text{°C}^{-1}\) and \(\alpha_2 = 70 \times 10^{-6} \, \text{°C}^{-1}\), respectively. The supports at A and C are rigid. Determine the lowest temperature at which the 3-mm gap is closed. Assume \(L_1 = 480 \, \text{mm}\) and \(L_2 = 580 \, \text{mm}\).#### Diagram:![Thermal Expansion Diagram](ThermalExpansionDiagram.png)The diagram shows two polymer bars labeled (1) and (2), with lengths \(L_1\) and \(L_2\) respectively. The gap \(g\) between the bars is 3 mm. Supports at points A and C are rigid.- Polymer Bar (1): Length \(L_1 = 480 \, \text{mm}\), Coefficient of thermal expansion \(\alpha_1 = 139 \times 10^{-6} \, \text{°C}^{-1}\)- Polymer Bar (2): Length \(L_2 = 580 \, \text{mm}\), Coefficient of thermal expansion \(\alpha_2 = 70 \times 10^{-6} \, \text{°C}^{-1}\)- Initial Temperature: 9°C- Gap: \(g = 3 \, \text{mm}\)#### Question:Determine the lowest temperature at which the 3-mm gap is closed.#### Answer:The temperature at which the 3-mm gap is closed is: \( \boxed{T} \) °CTo calculate, please refer to the connection of thermal expansion formula:\[ \Delta L = L \cdot \alpha \cdot \Delta T \]You will set the sum of expansions of both bars equal to the gap size (3 mm) to find \(\Delta T\) and then determine the temperature \(T\). #### Calculation Steps:1. Sum the expansions of both bars.2. Set the sum equal to the gap

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