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tekilochka [14]
3 years ago
15

An air bubble at the bottom of a lake 52.0 m deep has a volume of 1.50m^3. If the temperature at the bottom is 5.5 degree's Cels

ius and at the top is 18.5 degree's Celsius, what is the volume of the bubble just before it reaches the surface?
Physics
1 answer:
Artemon [7]3 years ago
6 0

Answer:

The volume of the bubble near the surface will be 9.47 m³

Explanation:

Given that,

Depth = 52.0 m

Volume = 1.50 m³

Temperature at bottom = 5.5°C

Temperature at the top = 18.5°C

We need to calculate the pressure at the depth 52.0 m

The pressure is

P_{1}=P_{2}+\rho gh

Where, P_{2} = Pressure at the surface

P_{1} = Pressure at the depth

Put the value into the formula

P_{1}=101325+(1000\times9.8\times52.0)

P_{1}=610925\ N/m^2

We need to calculate the volume of the bubble just before it reaches the surface

Using equation of ideal gas

PV=RT

\dfrac{PV}{T}=constant

Now, The equation of at bottom and top

\dfrac{P_{1}V_{1}}{T_{1}}=\dfrac{P_{2}V_{2}}{T_{2}}

V_{2}=\dfrac{P_{1}V_{1}T_{2}}{P_{2}T_{1}}

Put the value into the formula

V_{2}=\dfrac{610925\times1.50\times(18.5+273)}{101325\times(5.5+273)}

V=9.47\ m^3

Hence, The volume of the bubble near the surface will be 9.47 m³

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Complete Question

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