Suppose that an identical tank is filled with ethanol at 19.0°C and left to sit in – [Free] B80
Suppose that an identical tank is filled with ethanol at 19.0°C and left to sit in the sun instead of being placed underground. When the system reaches thermal equilibrium at 28.0°C, what do you expect the amount of ethanol that overflows from the tank to be?
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Question
Suppose that an identical tank is filled with ethanol at 19.0°C and left to sit in the sun instead of being placed underground. When the system reaches thermal equilibrium at 28.0°C, what do you expect the amount of ethanol that overflows from the tank to be?
- (a) Greater than Vair
- (b) Smaller than Vair
- (c) Equal to Vair
Answer
The correct answer is Smaller than Vair.
Detailed Explanation
When ethanol is heated, it expands due to thermal expansion. In the earlier scenario where the tank was underground, the tank itself remained nearly at the original temperature. Because the container volume did not expand, all the ethanol’s thermal expansion had to be accommodated by pushing liquid out of the tank. Therefore, the overflow volume was equal to the original air volume (Vair) present in the tank.
However, in this situation, the tank is exposed to sunlight. As the temperature rises from 19.0°C to 28.0°C, both the ethanol and the tank material expand:
- Ethanol: Has a relatively large coefficient of thermal expansion and therefore expands noticeably.
- Tank material: Also expands, increasing the capacity of the container itself.
Because the tank’s own volume increases, some of the ethanol’s expansion is accommodated by this extra capacity. In other words, the expanded tank absorbs part of the volume change.
As a result, the ethanol does not need to overflow as much as it would if the tank volume were fixed.
Conclusion
Therefore, the amount of ethanol that overflows from the sun-warmed tank is smaller than Vair.