- The linear coefficient of thermal expansion for concrete is 12×10^-6 degrees C. Consider a slab of concrete which is 4.0 m long and 0.0 degrees C. What is the change in length if the temperature is increased to 77 degrees F (Note that a conversion is necessary here) Show your work.
- What seems to be the primary safety concern in the lab?
- Why should you pay close attention to the dial gauge when the rod is expanding?
The Correct Answer and Explanation is:
Here are the answers and explanation for each question:
1. Thermal Expansion of Concrete
Given:
- Coefficient of linear expansion for concrete:
α=12×10−6 /∘C\alpha = 12 \times 10^{-6} \, /^\circ\text{C} - Initial length L0=4.0 m=400.0 cmL_0 = 4.0 \, \text{m} = 400.0 \, \text{cm}
- Initial temperature: T0=0∘CT_0 = 0^\circ\text{C}
- Final temperature: Tf=77∘FT_f = 77^\circ\text{F}
Step 1: Convert 77°F to °C T(∘C)=59(T(∘F)−32)=59(77−32)=59(45)=25∘CT(^\circ\text{C}) = \frac{5}{9}(T(^\circ\text{F}) – 32) = \frac{5}{9}(77 – 32) = \frac{5}{9}(45) = 25^\circ\text{C}
Step 2: Calculate change in temperature ΔT=Tf−T0=25∘C−0∘C=25∘C\Delta T = T_f – T_0 = 25^\circ\text{C} – 0^\circ\text{C} = 25^\circ\text{C}
Step 3: Use formula for linear expansion ΔL=α⋅L0⋅ΔT=(12×10−6)⋅400.0⋅25\Delta L = \alpha \cdot L_0 \cdot \Delta T = (12 \times 10^{-6}) \cdot 400.0 \cdot 25 ΔL=0.12 cm=1.2 mm\Delta L = 0.12 \, \text{cm} = 1.2 \, \text{mm}
Answer:
The change in length is 1.2 mm.
2. Primary Safety Concern in the Lab
The primary safety concern in the lab is preventing burns or injuries caused by heated materials and equipment, especially during thermal expansion experiments. When materials like rods or slabs are heated, they can reach temperatures that cause severe skin burns on contact. Additionally, fragile setups involving dial gauges, clamps, and heating elements can pose mechanical and electrical hazards if not handled carefully.
3. Why You Should Pay Close Attention to the Dial Gauge When the Rod Is Expanding
Correct Answer:
Because the dial gauge measures very small changes in length due to thermal expansion, and its readings are crucial to accurately understanding the material’s behavior under temperature changes.
300-Word Explanation:
In thermal expansion experiments, the dial gauge is a precision instrument used to detect and measure minute changes in length as a material is heated. When a rod or slab is exposed to rising temperatures, it expands linearly depending on its material properties. The amount of this expansion is often extremely small—sometimes on the order of tenths or hundredths of a millimeter—making it imperceptible to the naked eye. This is where the dial gauge becomes essential.
The dial gauge amplifies these small changes in length into readable mechanical movements, often measured in millimeters or thousandths of an inch. Paying close attention to this gauge is critical because even small misreadings can lead to incorrect calculations of the coefficient of linear expansion or total change in length. Inaccurate data can skew conclusions about the material’s properties and its behavior in real-world applications.
Furthermore, the dial gauge is usually attached to a fixed point while resting on the end of the expanding rod. If the apparatus is bumped or misaligned, it may produce faulty readings or damage the equipment. Careful observation ensures that any mechanical issues (e.g., sticking needles, backlash, or improper contact) are noticed immediately.
In lab settings, accurate data collection is key for analysis and comparison with theoretical values. Hence, close monitoring of the dial gauge ensures data integrity, reinforces safe handling practices, and helps build students’ proficiency in using precision instruments—an essential skill in engineering and scientific research.
Here are the answers and explanation for each question:
1. Thermal Expansion of Concrete
Given:
- Coefficient of linear expansion for concrete:
α=12×10−6 /∘C\alpha = 12 \times 10^{-6} \, /^\circ\text{C} - Initial length L0=4.0 m=400.0 cmL_0 = 4.0 \, \text{m} = 400.0 \, \text{cm}
- Initial temperature: T0=0∘CT_0 = 0^\circ\text{C}
- Final temperature: Tf=77∘FT_f = 77^\circ\text{F}
Step 1: Convert 77°F to °C T(∘C)=59(T(∘F)−32)=59(77−32)=59(45)=25∘CT(^\circ\text{C}) = \frac{5}{9}(T(^\circ\text{F}) – 32) = \frac{5}{9}(77 – 32) = \frac{5}{9}(45) = 25^\circ\text{C}
Step 2: Calculate change in temperature ΔT=Tf−T0=25∘C−0∘C=25∘C\Delta T = T_f – T_0 = 25^\circ\text{C} – 0^\circ\text{C} = 25^\circ\text{C}
Step 3: Use formula for linear expansion ΔL=α⋅L0⋅ΔT=(12×10−6)⋅400.0⋅25\Delta L = \alpha \cdot L_0 \cdot \Delta T = (12 \times 10^{-6}) \cdot 400.0 \cdot 25 ΔL=0.12 cm=1.2 mm\Delta L = 0.12 \, \text{cm} = 1.2 \, \text{mm}
Answer:
The change in length is 1.2 mm.
2. Primary Safety Concern in the Lab
The primary safety concern in the lab is preventing burns or injuries caused by heated materials and equipment, especially during thermal expansion experiments. When materials like rods or slabs are heated, they can reach temperatures that cause severe skin burns on contact. Additionally, fragile setups involving dial gauges, clamps, and heating elements can pose mechanical and electrical hazards if not handled carefully.
3. Why You Should Pay Close Attention to the Dial Gauge When the Rod Is Expanding
Correct Answer:
Because the dial gauge measures very small changes in length due to thermal expansion, and its readings are crucial to accurately understanding the material’s behavior under temperature changes.
300-Word Explanation:
In thermal expansion experiments, the dial gauge is a precision instrument used to detect and measure minute changes in length as a material is heated. When a rod or slab is exposed to rising temperatures, it expands linearly depending on its material properties. The amount of this expansion is often extremely small—sometimes on the order of tenths or hundredths of a millimeter—making it imperceptible to the naked eye. This is where the dial gauge becomes essential.
The dial gauge amplifies these small changes in length into readable mechanical movements, often measured in millimeters or thousandths of an inch. Paying close attention to this gauge is critical because even small misreadings can lead to incorrect calculations of the coefficient of linear expansion or total change in length. Inaccurate data can skew conclusions about the material’s properties and its behavior in real-world applications.
Furthermore, the dial gauge is usually attached to a fixed point while resting on the end of the expanding rod. If the apparatus is bumped or misaligned, it may produce faulty readings or damage the equipment. Careful observation ensures that any mechanical issues (e.g., sticking needles, backlash, or improper contact) are noticed immediately.
In lab settings, accurate data collection is key for analysis and comparison with theoretical values. Hence, close monitoring of the dial gauge ensures data integrity, reinforces safe handling practices, and helps build students’ proficiency in using precision instruments—an essential skill in engineering and scientific research.
