Answer :
Final answer:
The allowance for change in volume necessary for a change in temperature can be calculated using the formula for thermal expansion. In this case, the change in volume is approximately -0.182 ft³.
Explanation:
The problem is asking for the allowance for change in volume necessary for a temperature change. To solve this, we can use the formula for thermal expansion, which is given by:
ΔV = V₀αΔT
Where ΔV is the change in volume, V₀ is the initial volume, α is the coefficient of linear expansion, and ΔT is the change in temperature.
In this case, the initial volume is given as 20,000 ft³ and the change in temperature is from 115°F to -15°F. The coefficient of linear expansion for concrete is approximately 7 x 10^-6 /°F.
Substituting the values into the formula, we get:
- ΔV = (20,000 ft³)(7 x 10^-6 /°F)(-15°F - 115°F)
- ΔV = (20,000 ft³)(7 x 10^-6 /°F)(-130°F)
- ΔV = -182,000 x 10^-6 ft³/°F x ft³
- ΔV = -0.182 ft³
Therefore, the allowance for change in volume necessary for a temperature of -15°F is approximately -0.182 ft³.
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