What is the coefficient of linear expansion for a material that expands 0.01 m w

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Question: What is the coefficient of linear expansion for a material that expands 0.01 m when heated from 20°C to 100°C over a length of 2 m?

Options:

Correct Answer: 1 x 10^-4 /°C

Solution:

The coefficient of linear expansion α = ΔL / (L0 * ΔT) = 0.01 / (2 * 80) = 1.25 x 10^-5 /°C.

What is the coefficient of linear expansion for a material that expands 0.01 m when heated from 20°C to 100°C over a length of 2 m?

What is the coefficient of linear expansion for a material that expands 0.01 m when heated from 20°C to 100°C over a length of 2 m?

Step 1: Identify the change in length (ΔL). In this case, ΔL = 0.01 m.
Step 2: Identify the original length (L0). Here, L0 = 2 m.
Step 3: Identify the change in temperature (ΔT). The temperature changes from 20°C to 100°C, so ΔT = 100 - 20 = 80°C.
Step 4: Use the formula for the coefficient of linear expansion (α): α = ΔL / (L0 * ΔT).
Step 5: Substitute the values into the formula: α = 0.01 m / (2 m * 80°C).
Step 6: Calculate the denominator: 2 m * 80°C = 160 m°C.
Step 7: Now calculate α: α = 0.01 m / 160 m°C.
Step 8: Perform the division: α = 0.0000625 /°C.
Step 9: Convert to scientific notation: α = 1.25 x 10^-5 /°C.

Coefficient of Linear Expansion – The coefficient of linear expansion quantifies how much a material expands per unit length for each degree change in temperature.
Thermal Expansion Formula – The formula α = ΔL / (L0 * ΔT) is used to calculate the coefficient of linear expansion, where ΔL is the change in length, L0 is the original length, and ΔT is the change in temperature.