Explanation Given data: The depth of water is 50 m and diameter of bubble is 1.0 cm. Formula used: Write the expression for pressure of a liquid ( p ) . p = p 0 + ρ g d (1) Here, p 0 is pressure at the surface due to atmosphere, which is 1.013 × 10 5 Pa , ρ is density of liquid, g is gravity, which is 9.80 m s 2 , and d is depth of liquid. Write the expression for relationship between before and after conditions of ideal gas. p 2 V 2 T 2 = p 1 V 1 T 1 (2) Here, p 1 is pressure in first condition, V 1 is volume in first condition, T 1 is temperature in first condition, p 2 is pressure in second condition, V 2 is volume in second condition, and T 2 is temperature in second condition, Write the expression for volume of sphere ( V ) . V = 4 π 3 r 3 (3) Here, r is radius. Explanation: Refer to Table 13.1 in the textbook for the densities of fluids at 1 atm pressure. From table 13.1, the density of water is 1000 kg m 3 . Consider the air bubble is at thermal equilibrium all the time and air inside the bubble is ideal gas. Substitute 1.013 × 10 5 Pa for p 0 , 1000 kg m 3 for ρ , 9.80 m s 2 for g , and 50 m for d in equation (1), p = 1.013 × 10 5 Pa + ( 1000 kg m 3 ) ( 9.80 m s 2 ) ( 50 m ) = 101300 Pa + 490000 Pa = 5.913 × 10 5 Pa Modify equation (3) for bubble in deep water. V 1 = 4 π 3 r 1 3 Here, V 1 is volume of bubble in deep water, and r 1 is radius of bubble in deep water. Modify equation (3) for bubble at surface. V 2 = 4 π 3 r 2 3 Here, V 2 is volume of bubble at surface, and r 2 is radius of bubble at surface. Find the radius of bubble in deep water ( r 1 ) . r 1 = 1.0 cm 2 = 0.5 cm Re-arrange the equation (2)

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Variation of pressure

From the equation of pressure, pressure is directly proportional to the applied force.

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Chapter 13, Problem 56GP

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The diameter of bubble when it reaches the surface of the lake.

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Chapter 13, Problem 55GP

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Chapter 13 Solutions

College Physics: A Strategic Approach (4th Edition)

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Ch. 13 - Prob. 11CQ Ch. 13 - Imagine a square column of the atmosphere, 1 m on...Ch. 13 - Prob. 13CQ Ch. 13 - Prob. 14CQ Ch. 13 - A beaker of water rests on a scale. A metal ball...Ch. 13 - Prob. 16CQ Ch. 13 - Prob. 17CQ Ch. 13 - Prob. 18CQ Ch. 13 - A heavy lead block and a light aluminum block of...Ch. 13 - When you place an egg in water, it sinks. If you...Ch. 13 - The water of the Dead Sea is extremely salty,...Ch. 13 - Fish can adjust their buoyancy with an organ...Ch. 13 - Prob. 23CQ Ch. 13 - Prob. 24CQ Ch. 13 - Prob. 25CQ Ch. 13 - Prob. 27CQ Ch. 13 - Prob. 28CQ Ch. 13 - Is it possible for a fluid in a tube to flow in...Ch. 13 - Prob. 31CQ Ch. 13 - Prob. 32MCQ Ch. 13 - Figure Q.13.33 shows a 100 g block of copper ( =...Ch. 13 - Masses A and B rest on very light pistons that...Ch. 13 - Prob. 35MCQ Ch. 13 - Prob. 36MCQ Ch. 13 - A large beaker of water is filled to its rim with...Ch. 13 - Prob. 38MCQ Ch. 13 - Prob. 40MCQ Ch. 13 - An object floats in water, with 75% of its volume...Ch. 13 - Prob. 42MCQ Ch. 13 - Water flows through a 4.0-cm-diameter horizontal...Ch. 13 - A 15-m-long garden hose has an inner diameter of...Ch. 13 - Prob. 1P Ch. 13 - Prob. 2P Ch. 13 - A standard gold bar stored at Fort Knox, Kentucky,...Ch. 13 - Prob. 4P Ch. 13 - Prob. 5P Ch. 13 - Prob. 6P Ch. 13 - Prob. 7P Ch. 13 - Prob. 8P Ch. 13 - A tall cylinder contains 25 cm of water. Oil is...Ch. 13 - A 35-cm-tall, 5.0-cm-diameter cylindrical beaker...Ch. 13 - The gauge pressure at the bottom of a cylinder of...Ch. 13 - Prob. 12P Ch. 13 - A research submarine has a 20-cm-diameter window...Ch. 13 - The highest that George can suck water up a very...Ch. 13 - Prob. 15P Ch. 13 - Prob. 16P Ch. 13 - Prob. 17P Ch. 13 - Glycerin is poured into an open U-shaped tube...Ch. 13 - A U-shaped tube, open to the air on both ends,...Ch. 13 - What is the height of a water barometer at...Ch. 13 - A cargo barge is loaded in a saltwater harbor for...Ch. 13 - Prob. 22P Ch. 13 - A 10 cm 10 cm 10 cm wood block with a density of...Ch. 13 - What is the tension in the string in Figure...Ch. 13 - What is the tension in the string in Figure...Ch. 13 - To determine an athletes body fat, she is weighed...Ch. 13 - Prob. 28P Ch. 13 - Styrofoam has a density of 32 kg/m3. What is the...Ch. 13 - Prob. 30P Ch. 13 - Calculate the buoyant force due to the surrounding...Ch. 13 - Prob. 32P Ch. 13 - Water flowing through a 2.0-cm-diameter pipe can...Ch. 13 - Prob. 34P Ch. 13 - Prob. 35P Ch. 13 - Prob. 37P Ch. 13 - Prob. 39P Ch. 13 - Prob. 40P Ch. 13 - What pressure difference is required between the...Ch. 13 - Prob. 42P Ch. 13 - Water flows at 0.25 L/s through a 10-m-long garden...Ch. 13 - Prob. 44P Ch. 13 - Prob. 45P Ch. 13 - Prob. 47P Ch. 13 - Prob. 48P Ch. 13 - Prob. 49P Ch. 13 - Prob. 50P Ch. 13 - As discussed in Section 13.3, a persons percentage...Ch. 13 - The density of aluminum is 2700 kg/m3. How many...Ch. 13 - An oil layer floats on 85 cm of water in a tank....Ch. 13 - Prob. 55GP Ch. 13 - Prob. 56GP Ch. 13 - A sphere completely submerged in water is tethered...Ch. 13 - Prob. 58GP Ch. 13 - A 5.0 kg rock whose density is 4800 kg/m3 is...Ch. 13 - A flat slab of styrofoam, with a density of 32...Ch. 13 - A 2.0 mL syringe has an inner diameter of 6.0 mm,...Ch. 13 - Prob. 62GP Ch. 13 - The leaves of a tree lose water to the atmosphere...Ch. 13 - II A hurricane wind blows across a 6.00 m 5.0 m...Ch. 13 - Prob. 65GP Ch. 13 - Prob. 66GP Ch. 13 - Prob. 67GP Ch. 13 - Prob. 68GP Ch. 13 - Prob. 69GP Ch. 13 - Smoking tobacco is bad for your circulatory...Ch. 13 - A stiff, 10-cm-long tube with an inner diameter of...Ch. 13 - Suppose that in response to some stimulus a small...Ch. 13 - Prob. 73MSPP Ch. 13 - Prob. 75MSPP

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The diameter of bubble when it reaches the surface of the lake.

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Chapter 13 Solutions