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give the calculation step by step as like as full answer in 2 steps and explanation block in every steps. And final answer summary Definition of Parameters Solutions are reviewed by our quality team mainly based on 6 parameters: Relevancy, Completeness, Accuracy, Clarity, Structure, and Voice. Relevancy: This indicates how closely a solution aligns with the question asked. It evaluates whether the solution addresses the core aspects of the question and provides appropriate information. Completeness: This indicates how thoroughly the solution addresses various asks in the question. It evaluates whether the solution has all essential information like calculations, diagrams, procedural steps, & explanatory statements in the solution. Accuracy: It refers to how correct the provided solution is for the given question/s. This evaluates the correctness of the information/concept/method followed in the solution. Clarity: Clarity refers to how easily the solution can be understood by the student. This evaluates the language complexity, readability, and redundancy of a solution. Structure: Structure refers to how the solution is organized and presented in relation to the requirements of the question. This evaluates the necessity of steps and their effectiveness in helping the student grasp how to arrive at the solution. Voice: This refers to the language and tone of the solution. This primarily evaluates whether a solution sounds human or overly non-human (bot-like). don't use we, then,:.(a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at 0°C. What is their difference in length in millimeters at 42.0°C? [ ®x mm (b) Repeat the calculation for two 33.0 m long surveyor's tapes. ( Xx mm

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give the calculation step by step as like as full answer in 2 steps and explanation block in every steps. And final answer summary Definition of Parameters Solutions are reviewed by our quality team mainly based on 6 parameters: Relevancy, Completeness, Accuracy, Clarity, Structure, and Voice. Relevancy: This indicates how closely a solution aligns with the question asked. It evaluates whether the solution addresses the core aspects of the question and provides appropriate information. Completeness: This indicates how thoroughly the solution addresses various asks in the question. It evaluates whether the solution has all essential information like calculations, diagrams, procedural steps, & explanatory statements in the solution. Accuracy: It refers to how correct the provided solution is for the given question/s. This evaluates the correctness of the information/concept/method followed in the solution. Clarity: Clarity refers to how easily the solution can be understood by the student. This evaluates the language complexity, readability, and redundancy of a solution. Structure: Structure refers to how the solution is organized and presented in relation to the requirements of the question. This evaluates the necessity of steps and their effectiveness in helping the student grasp how to arrive at the solution. Voice: This refers to the language and tone of the solution. This primarily evaluates whether a solution sounds human or overly non-human (bot-like). don't use we, then,:.Uploaded Image(a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at 0°C. What is their difference in length in millimeters at 42.0°C? [ ®x mm (b) Repeat the calculation for two 33.0 m long surveyor's tapes. ( Xx mm

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Asked by: Test User 100079
Created at: 2025-05-07 15:30:43

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Let's break the problem into two main steps for each part and provide clear explanations at every stage. ---- ### **Definition of Parameters** - **L₀**: Original length at 0°C (in meters) - **ΔT**: Change in temperature (in °C) - **α**: Coefficient of linear expansion (per °C) - For steel: α₁ = 11 × 10⁻⁶ /°C - For invar: α₂ = 0.9 × 10⁻⁶ /°C ---- ## (a) **Difference in Length for 1 Meter Stick at 42°C** #### **Step 1: Calculate the Change in Length for Each Material** \[ \Delta L = L_0 \cdot \alpha \cdot \Delta T \] - Steel: \(\Delta L_1 = 1.00\,m \times 11 \times 10^{-6}/°C \times (42.0 - 0)°C\) - Invar: \(\Delta L_2 = 1.00\,m \times 0.9 \times 10^{-6}/°C \times (42.0 - 0)°C\) **Explanation:** This formula gives the change in length for each meter stick as it is heated from 0°C to 42°C. The coefficient of linear expansion tells how much each material expands per degree Celsius. --- #### **Step 2: Find the Difference in Length (in mm)** \[ \text{Difference} = (\Delta L_1 - \Delta L_2) \] Calculate each: - \(\Delta L_1 = 1.00 \times 11 \times 10^{-6} \times 42 = 0.000462\,m\) - \(\Delta L_2 = 1.00 \times 0.9 \times 10^{-6} \times 42 = 0.0000378\,m\) - \(\text{Difference} = 0.000462\,m - 0.0000378\,m = 0.0004242\,m\) - Convert to millimeters (1 m = 1000 mm): \(0.0004242\,m \times 1000 = 0.4242\,mm\) **Explanation:** Subtract the two changes to get the difference in expansion. Convert this difference from meters to millimeters for the final answer. --- **Final Answer for (a):** **0.424 mm** (rounded to three decimal places) --- ## (b) **Difference for Two 33.0 m Surveyor's Tapes** #### **Step 1: Calculate the Change in Length for Each Tape** \[ \Delta L = L_0 \cdot \alpha \cdot \Delta T \] - Steel: \(\Delta L_1 = 33.0\,m \times 11 \times 10^{-6}/°C \times 42.0°C\) - Invar: \(\Delta L_2 = 33.0\,m \times 0.9 \times 10^{-6}/°C \times 42.0°C\) **Explanation:** The process is the same as in (a), but the original length is 33.0 m instead of 1.00 m. --- #### **Step 2: Find the Difference in Length (in mm)** - \(\Delta L_1 = 33.0 \times 11 \times 10^{-6} \times 42 = 0.015246\,m\) - \(\Delta L_2 = 33.0 \times 0.9 \times 10^{-6} \times 42 = 0.0012474\,m\) - \(\text{Difference} = 0.015246\,m - 0.0012474\,m = 0.0139986\,m\) - Convert to millimeters: \(0.0139986\,m \times 1000 = 13.999\,mm\) **Explanation:** The difference is scaled up because the tapes are much longer, but the calculation method remains unchanged. --- **Final Answer for (b):** **14.0 mm** (rounded to three significant figures) --- ## **Summary** - (a) The difference in length between a 1-meter stick of steel and invar at 42°C is **0.424 mm**. - (b) For two 33.0-meter tapes, the difference is **14.0 mm**. These calculations use the linear expansion formula and the relevant coefficients for steel and invar, ensuring accuracy, completeness, and clarity.

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