A copper wire has an original length of 3 meters. If the wire undergoes a temperature increase, and its final length is measured to be 3.012 meters, what was the change in temperature? (The coefficient of linear thermal expansion for copper is 1.7×10−5 per degree Celsius).
Question
A copper wire has an original length of 3 meters. If the wire undergoes a temperature increase, and its final length is measured to be 3.012 meters, what was the change in temperature? (The coefficient of linear thermal expansion for copper is 1.7×10−5 per degree Celsius).
Solution
The formula for linear thermal expansion is:
ΔL = α * L0 * ΔT
where: ΔL is the change in length, α is the coefficient of linear thermal expansion, L0 is the original length, and ΔT is the change in temperature.
We can rearrange this formula to solve for ΔT:
ΔT = ΔL / (α * L0)
Substituting the given values:
ΔT = (3.012 m - 3 m) / (1.7×10−5 /°C * 3 m) ΔT = 0.012 m / (5.1×10−5 m/°C) ΔT = 235.29 °C
So, the change in temperature was approximately 235.29 degrees Celsius.
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