Linear thermal expansion (in one dimension)
1) the change in length δl is proportional to the original length l, and the change in temperature δt : δl = αlδt, where δl is the change in length , and α is the coefficient of linear expansion.
a) the main span of san francisco’s golden gate bridge is 1275 m long at its coldest (–15ºc). the coefficient of linear expansion, α , for steel is 12×10−6 /ºc. when the temperatures rises to 25 °c, what is its change in length in meters?
2) the change in volume δv is very nearly δv ≈ 3αvδt . this equation is usually written as δv = βvδt, where β is the coefficient of volume expansion and β ≈ 3α . v is the original volume. δt is the change in temperature. suppose your 60.0-l (15.9-gal) steel gasoline tank is full of gasoline, and both the tank and the gasoline have a temperature of 15.0ºc . the coefficients of volume expansion, for gasoline is βgas = 950×10−6 /ºc , for the steel tank is βsteel = 35×10−6 /ºc .
a) what is the change in volume (in liters) of the gasoline when the temperature rises to 25 °c in l?
b) what is the change in volume (in liters) of the tank when the temperature rises to 25 °c in l?
c) how much gasoline would be spilled in l?