Consider a liquid in a container which is open to the atmosphere. We can assume that its temperature does not change with depth. a) Show that a vertical column of the liquid with cross-sectional area A has a weight of ph. Ag at depth h, where p is the liquid's density and g is the acceleration due to gravity. Hence calculate the additional pressure of the liquid at depth h over and above the air pressure at the surface of the liquid. (Think about forces and accelerations. Is the column of water accelerating?) b) A bubble of gas in the liquid rises to the surface from a depth of h. Show that the fractional increase in the volume of the bubble is pgh/Ps where Ps is the atmospheric pressure at the surface of the liquid. You should assume the bubble obeys the ideal gas law.

University Physics Volume 2
18th Edition
ISBN:9781938168161
Author:OpenStax
Publisher:OpenStax
Chapter1: Temperature And Heat
Section: Chapter Questions
Problem 48P: A person taking a reading of the temperature in a freezer in Celsius makes two mistakes: first...
icon
Related questions
icon
Concept explainers
Question
Consider a liquid in a container which is open to the atmosphere. We can assume that its temperature does not change with depth.
a) Show that a vertical column of the liquid with cross-sectional area A has a weight of ph.Ag at depth h, where p is the liquid's density and gis
the acceleration due to gravity. Hence calculate the additional pressure of the liquid at depth h over and above the air pressure at the surface of
the liquid. (Think about forces and accelerations. Is the column of water accelerating?)
b) A bubble of gas in the liquid rises to the surface from a depth of h. Show that the fractional increase in the volume of the bubble is
pgh/Ps where Ps is the atmospheric pressure at the surface of the liquid. You should assume the bubble obeys the ideal gas law.
Transcribed Image Text:Consider a liquid in a container which is open to the atmosphere. We can assume that its temperature does not change with depth. a) Show that a vertical column of the liquid with cross-sectional area A has a weight of ph.Ag at depth h, where p is the liquid's density and gis the acceleration due to gravity. Hence calculate the additional pressure of the liquid at depth h over and above the air pressure at the surface of the liquid. (Think about forces and accelerations. Is the column of water accelerating?) b) A bubble of gas in the liquid rises to the surface from a depth of h. Show that the fractional increase in the volume of the bubble is pgh/Ps where Ps is the atmospheric pressure at the surface of the liquid. You should assume the bubble obeys the ideal gas law.
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Energy transfer
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
University Physics Volume 2
University Physics Volume 2
Physics
ISBN:
9781938168161
Author:
OpenStax
Publisher:
OpenStax
University Physics Volume 1
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
Physics for Scientists and Engineers: Foundations…
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Glencoe Physics: Principles and Problems, Student…
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill