Thermodynamics expansion problem

AI Thread Summary
The problem involves calculating the depth of a swimming pool that overflows when water warms from 24 °C to 34 °C. The volume expansion coefficient for water is given as 2.07 x 10^-4 °C−1. The initial attempt incorrectly equated the change in depth (1.2 cm) with the change in volume. Clarification revealed that the change in volume should be calculated using the volume expansion formula, and the correct approach does not require taking the cube root. The user successfully found the correct answer after receiving guidance.
xnitexlitex
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Homework Statement


On a hot summer day, a cubical swimming pool is filled to within 1.2 cm of the top with water at 24 °C. When the water warms to 34 °C, the pool overflows. What is the depth of the pool? (The volume expansion coefficient for water is 2.07 10-4 °C−1.)


Homework Equations


ΔV = βV0ΔT


The Attempt at a Solution


I set ΔV equal to 1.2, plugged the numbers in, got 193.24 cm3 for the volume, and took the cube root of the result for the depth. That didn't work. What am I supposed to do?
 
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Hi xnitexlitex! :smile:

ΔV is not equal to 1.2.
1.2 cm is the change in depth, not the change in volume.

How did you plug your numbers in and get your volume?
Because I see no reason why you would need to take a cube root...
 
Thank you. I just got the answer now.
 

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