Thermodynamics: The Physics of Heat Name:__________________

Mr. Miller **Linear Expansion Worksheet**

Formula for Linear Expansion: **ΔL = aLΔt ** where:

ΔL = the change in length

a = the coefficient of linear expansion for the material

L = the original length

Δt = the change in temperature

- A 10,000 meter steel railroad track with a coefficient of linear expansion of 12 x 10-6 per degree Celsius changes temperature from 18°C to 38°C. By how many meters will the railroad tracks expand?

- Why do you think railroad tracks are segmented into short pieces?

- The Eiffel Tower in Paris is 324 meters tall, and is made primarily of iron, which has a coefficient of linear expansion of 12 x 10-6. The coldest temperature ever recorded in Paris was 1°C, and the hottest was 99°C. What is the change in length that the tower has experienced in its lifetime?

- By how much would you need to heat a 10 foot bar of zinc to make it expand by one inch? The coefficient of linear expansion of zinc is 30 x 10-6 per degree Celsius.

- A metal bar changes in length by 1 meter with a 150 degree Celsius change in temperature. It’s coefficient of linear expansion is 25 x 10-6 per degree Celsius. What is the metal bar’s original length?

- An unknown metal alloy is being tested to discover its thermal properties to see if it is suitable for use as a component in an aircraft wing. The alloy is formed into a bar measuring 1 meter in length, and is then heated from its starting temperature of 30 degrees Celsius to a final temperature of 100 degrees Celsius. The length of the heated bar is measured to be exactly 1.002 meters in length. What is the coefficient of thermal expansion of the alloy?

EXTRA CREDIT:

- The aircraft wing from problem 6 experiences temperature extremes that span 210 degrees Celsius. The component for the wing will have a length of exactly 3 meters. Testing indicates that the aircraft wing will remain stable only if the component never expands to a length larger than 3.017 meters. If the component is made from the metal alloy in question, will it meet this requirement?