A hole is drilled through a copper plate whose temperature is 17.2 °C. When the plate is heated to 191 °C, by what fraction (r-ro)/ro will the radius of the hole change?
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delta L /L = k * delta T
To determine the fractional change in radius of the hole, we can use the concept of thermal expansion. The change in radius of the hole can be calculated using the formula:
Δr = α * r * ΔT
where:
Δr is the change in radius
α is the coefficient of linear expansion of copper
r is the initial radius of the hole
ΔT is the change in temperature
The coefficient of linear expansion for copper is approximately 0.0000168 per degree Celsius.
Now, we can substitute the given values into the formula and solve for Δr:
ΔT = 191 °C - 17.2 °C = 173.8 °C
α = 0.0000168 per °C
r = initial radius of the hole (unknown)
From the given problem, we want to find the fractional change, which is expressed as (Δr - r0) / r0. Since we don't have the value of r0, we can express the equation as (Δr / r).
Therefore, the fractional change in radius will be:
(Δr / r) = (α * r * ΔT) / r
(Δr / r) = α * ΔT
Substituting the known values:
(Δr / r) = 0.0000168 per °C * 173.8 °C
By multiplying these numbers, the units will cancel out, leaving only the fractional change in radius.