Multiple-Concept Example 4 deals with the concepts used in this problem. Conceptual Example 3 is also pertinent. A bubble, located 0.263 m beneath the surface in a glass of beer, rises to the top. The air pressure at the top is 1.01 x 10 Pa. Assume that the density of beer is the same as that of fresh water. If the temperature and number of moles of CO, remain constant as the bubble rises, find the ratio of its volume at the top to that at the bottom.

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Chapter1: Units, Trigonometry. And Vectors
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### Problem Statement

**Title: Volume Ratio of CO₂ Bubble in Beer**

*Multiple-Concept Example 4* deals with the concepts used in this problem. *Conceptual Example 3* is also pertinent. 

A bubble, located 0.263 m beneath the surface in a glass of beer, rises to the top. The air pressure at the top is \( 1.01 \times 10^5 \) Pa. Assume that the density of beer is the same as that of fresh water. If the temperature and number of moles of CO₂ remain constant as the bubble rises, find the ratio of its volume at the top to that at the bottom.

### Explanation of Diagram

The image features a vertical glass filled with a liquid, representing beer. A dashed vertical line is drawn from the top to a point near the bottom of the glass, indicating the path of a rising CO₂ bubble. The label "h" is marked on this line, signifying the depth at which the bubble is initially located below the surface of the liquid, in this case, 0.263 meters.

### Parameters:
- Depth (h): 0.263 meters
- Surface Pressure: \( 1.01 \times 10^5 \) Pa

### Required:
Find the ratio of the bubble’s volume at the top (surface) to that at its initial position (0.263 m beneath the surface).

### Notes:
Temperature and number of moles of CO₂ are constant, and density of beer is assumed to be the same as that of fresh water for simplicity.
Transcribed Image Text:### Problem Statement **Title: Volume Ratio of CO₂ Bubble in Beer** *Multiple-Concept Example 4* deals with the concepts used in this problem. *Conceptual Example 3* is also pertinent. A bubble, located 0.263 m beneath the surface in a glass of beer, rises to the top. The air pressure at the top is \( 1.01 \times 10^5 \) Pa. Assume that the density of beer is the same as that of fresh water. If the temperature and number of moles of CO₂ remain constant as the bubble rises, find the ratio of its volume at the top to that at the bottom. ### Explanation of Diagram The image features a vertical glass filled with a liquid, representing beer. A dashed vertical line is drawn from the top to a point near the bottom of the glass, indicating the path of a rising CO₂ bubble. The label "h" is marked on this line, signifying the depth at which the bubble is initially located below the surface of the liquid, in this case, 0.263 meters. ### Parameters: - Depth (h): 0.263 meters - Surface Pressure: \( 1.01 \times 10^5 \) Pa ### Required: Find the ratio of the bubble’s volume at the top (surface) to that at its initial position (0.263 m beneath the surface). ### Notes: Temperature and number of moles of CO₂ are constant, and density of beer is assumed to be the same as that of fresh water for simplicity.
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