A brass box is in the shape of a cube. The coefficient of linear thermal expansion is 19 × 10−6/°C. If the temperature of the box is increased by 20°C, then what is the fractional change in the volume of the box?
Question
A brass box is in the shape of a cube. The coefficient of linear thermal expansion is 19 × 10−6/°C. If the temperature of the box is increased by 20°C, then what is the fractional change in the volume of the box?
Solution
The fractional change in volume of a solid due to a change in temperature can be calculated using the formula:
ΔV/V = βΔT
where:
- ΔV/V is the fractional change in volume,
- β is the coefficient of volume expansion, and
- ΔT is the change in temperature.
For a solid, the coefficient of volume expansion is approximately three times the coefficient of linear expansion (α). So, β ≈ 3α.
Given that the coefficient of linear expansion (α) is 19 × 10−6/°C and the change in temperature (ΔT) is 20°C, we can substitute these values into the formula:
ΔV/V = 3αΔT ΔV/V = 3 * 19 × 10−6/°C * 20°C ΔV/V = 1.14 × 10−3
So, the fractional change in the volume of the brass box when the temperature is increased by 20°C is approximately 1.14 × 10−3, or 0.00114.
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