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Rufina [12.5K]
2 years ago
13

A bubble, located 0.200 m beneath the surface in a glass of beer, rises to the top. The air pressure at the top is 1.01x10⁵ Pa.

Assume that the density of beer is the same as that of fresh water. If the temperature and number of moles of CO₂ in the bubble remain constant as the bubble rises, find the ratio of the bubble's volume at the top to its volume at the bottom.
Physics
1 answer:
Cerrena [4.2K]2 years ago
6 0

Answer:

\frac{1.019}{1}

Explanation:

To solve this equation we will have to consider that the bubble is filled with an Ideal Gas and as such we can use the Ideal Gas Law

PV = nRT

Where

P = Pressure

V = Volume

n = Moles

R = Ideal Gas Constant

T  = Temperature

Now since we know that the value for the temperature and moles is constant we can simply use Boyles Law for the two states

P_{1} V_{1} =P_{2} V_{2}

Let us look at the two states

State 1 (at top)

Pressure = 1.01*10^5

Volume = V_{1}

State 2 (at bottom)

Pressure = 1.01*10^5 + dgh

Where

d = Density of liquid (1000 kg/m³)

d = Acceleration due to gravity (9.8 m/s²)

d = Height of liquid (0.200 m)

Pressure = 102,962

Volume = V_{2}

Inputting these values into the Boyles Law

P_{1} V_{1} =P_{2} V_{2}\\ (101000)V_{1} = (102962)V_{2}\\ \frac{V_{1}}{V_{2}} = \frac{102962}{101000} \\  \frac{V_{1}}{V_{2}} = \frac{1.019}{1}

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