Final answer:
Approximately 0.091 gallons (or 345 milliliters) of carbon tetrachloride will spill over when the temperature rises from 7°C to 43°C in a 45-gallon steel container.
Step-by-step explanation:
The question asks how much carbon tetrachloride will spill over when the temperature rises from 7°C to 43°C in a 45-gallon steel container. To find the amount spilled, we need to calculate the volume change of the carbon tetrachloride using the average volume coefficient of expansion. Since the steel container is held at a constant temperature, its volume remains constant. We can use the equation for volume expansion to calculate the change in volume of the carbon tetrachloride:
ΔV = V₀ * β * ΔT
where:
- ΔV is the change in volume of the carbon tetrachloride
- V₀ is the initial volume of the carbon tetrachloride
- β is the volume coefficient of expansion of the carbon tetrachloride
- ΔT is the change in temperature
In this case, the initial volume (V₀) is 45 gallons, the temperature change (ΔT) is (43°C - 7°C) = 36°C, and the volume coefficient of expansion (β) is 0.000581(°C)⁻¹. Plugging these values into the equation, we can calculate the change in volume:
ΔV = 45 * 0.000581 * 36
Calculating ≈ 0.091 gallons. Therefore, approximately 0.091 gallons (or 345 milliliters) of carbon tetrachloride will spill over when the temperature rises to 43°C.