Fused quartz possesses an exceptionally low coefficient of linear expansion, −15.50×10−7 (∘C)−1. Suppose a bar of fused quartz of length 3.23 m at 20.0 ∘C is heated to 227 ∘C. By how much, in millimeters, would the bar expand?
To find out how much the bar of fused quartz expands, we can use the following formula:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length of the bar
ΔT is the change in temperature
Let's plug in the given values:
α = -15.50 × 10^(-7) (°C)^(-1) (the negative sign indicates contraction)
L = 3.23 m
ΔT = 227 °C - 20 °C = 207 °C
ΔL = (-15.50 × 10^(-7) (°C)^(-1)) * (3.23 m) * (207 °C)
Now, let's calculate the result:
ΔL = -10.07 × 10^(-3) m
To convert the result to millimeters, we can multiply it by 1000:
ΔL = -10.07 × 10^(-3) m * 1000 = -10.07 mm
Therefore, the bar of fused quartz would contract by 10.07 millimeters.