A spherical air bubble in a lake expands as it rises slowly to the surface. At t

Question

A spherical air bubble in a lake expands as it rises slowly to the surface. At the point it starts to rise, the pressure is 2.00 atm, the temperature of the water is 10.0 C, and the radius of the bubble is5.00 × 103 m. At the surface, the pressure is1.00 atm and the temperature of the water is20.0 C.

Part A

What is the final-to-initial volume ratio for the expanding bubble?

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Part B

What is the change in thermal energy of the bubble?

Express your answer with the appropriate units.

A spherical air bubble in a lake expands as it rises slowly to the surface. At the point it starts to rise, the pressure is 2.00 atm, the temperature of the water is 10.0 C, and the radius of the bubble is5.00 × 103 m. At the surface, the pressure is1.00 atm and the temperature of the water is20.0 C.

Part A

What is the final-to-initial volume ratio for the expanding bubble?

Vf/Vi=

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Part B

What is the change in thermal energy of the bubble?

Express your answer with the appropriate units.

Eth=

Explanation / Answer

Here,

P1 = 2 atm

T1 = 10 degree C = 283 K

P2 = 1 atm

T2 = 20 degree C = 293 K

r1 = 5 *10^-3 m

A)

for the ratio of volume

Using ideal gas equation

P2 * V2/T2 = P1 * V1/T1

2 * V1/283 = 1 * V2/293

V2/V1 = Vf/Vi = 2.071

the final-to-initial volume ratio for the expanding bubble is 2.071

part B)

as P * V = n * R * T

2 * 1.01 *10^5 * pi * (4/3) * (0.005)^3 = n * 8.314 * 283

n = 4.495 *10^-5 moles

change in thermal energy of bubble = 1.5 * n * R * del T

change in thermal energy of bubble = 1.5 ( 4.495 *10^-5) * 8.314 * (10)

change in thermal energy of bubble = 5.606 *10^-3 J

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