Thermodynamics expansion problem

In summary, the conversation discusses determining the depth of a cubical swimming pool filled with water at 24 °C, given that it overflows when the water warms to 34 °C. The volume expansion coefficient for water is provided as 2.07 x 10^-4 °C^-1. The solution involves setting the change in volume equal to 1.2 cm, plugging in the numbers and solving for the volume, and then taking the cube root to find the depth. However, it is clarified that 1.2 cm is the change in depth, not the change in volume. After correcting this, the correct answer is obtained.
  • #1
xnitexlitex
23
0

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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  • #2
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...
 
  • #3
Thank you. I just got the answer now.
 

FAQ: Thermodynamics expansion problem

What is thermodynamics expansion problem?

Thermodynamics expansion problem refers to the study of the behavior of gases and liquids when they expand or contract due to changes in temperature, pressure, or volume. It involves the application of the laws of thermodynamics to understand and predict the changes in the state of a substance during expansion or contraction.

What are the three types of thermodynamic expansion?

The three types of thermodynamic expansion are isothermal expansion, adiabatic expansion, and isobaric expansion. Isothermal expansion occurs at a constant temperature, adiabatic expansion occurs without any exchange of heat, and isobaric expansion occurs at a constant pressure.

What is the ideal gas law and how is it related to thermodynamic expansion?

The ideal gas law is a fundamental law of thermodynamics that describes the relationship between pressure, volume, temperature, and the number of moles of a gas. It states that the product of pressure and volume is directly proportional to the product of temperature and the number of moles. This law is often used to analyze thermodynamic expansion problems.

What is the difference between reversible and irreversible expansion?

In reversible expansion, the changes in the state of a substance can be reversed by reversing the external conditions that caused the expansion. This means that the system and its surroundings can return to their initial state without any loss of energy. In irreversible expansion, the changes in the state of a substance cannot be reversed, and some energy is lost to the surroundings.

How is thermodynamic expansion used in real-life applications?

Thermodynamic expansion has many practical applications, such as in the design of heat engines, refrigeration systems, and power plants. It is also used in the production of industrial gases, such as nitrogen and oxygen. Understanding thermodynamic expansion is crucial in various industries, including aerospace, automotive, and chemical, to optimize processes and improve efficiency.

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