Final answer:
By using the volume coefficient of expansion for carbon tetrachloride, we determine that 0.82 gallons of carbon tetrachloride will spill over when the temperature rises from 6°C to 30°C.
Step-by-step explanation:
The student's question pertains to the concept of thermal expansion, which is a physical property of matter wherein the matter changes its volume in response to a change in temperature. When a substance such as carbon tetrachloride is heated, it expands, and if contained within a rigid container whose volume does not change, some of the substance will be forced out of the container. The volume change can be calculated using the volume coefficient of expansion for the substance and the temperature change.
The formula to calculate the volume change of the liquid is:
\∆V = βV_0∆T)
Where:
- \(∆V\) is the change in volume
- \(β\) is the volume coefficient of expansion
- \(V_0\) is the original volume
- \(∆T\) is the change in temperature
By applying this formula to the given values:
(∆V = 0.000581(\frac{1}{°C})(59 gal)(30°C - 6°C)
∆V = 0.000581 \times 59 \times 24
∆V = 0.82 gal
Therefore, 0.82 gallons of carbon tetrachloride will spill over when the temperature rises to 30°C.