Respuesta :
The volume of the bubble as it reaches the surface is 4.8 cm³.
What is volume?
The area that any three-dimensional solid occupies is known as its volume.
What is pressure ?
Area-per-force force applied. P=FA, where F is the force operating perpendicular to the surface area A, gives it mathematical expression. The pascal (Pa), which equates to a newton per square meter (N/m 2), is the accepted unit of pressure.
The concepts used to solve this problem are variation of pressure with depth in a fluid and ideal gas equation.
First use relation of atmospheric pressure and static fluid pressure to calculate the pressure at the bottom.
Finally use the ideal gas equation to calculate the volume of the bubble as it reaches the surface.
If a fluid is within a container then the depth of an object placed in that fluid can be measured.
Expression for the pressure at the depth is,
P₁= Patm + Pgauge
Here,
Patm
P₁ is the pressure at the surface,
Patm is the atmospheric pressure
P gauge is the is the gauge pressure.
Gas inside the bubble behaves like an ideal gas.
Expression for the ideal gas law is,
PV= nRT
Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Pressure at the surface of the lake is equal to the atmospheric pressure.
P₁= Patm
Here
V₁= is the volume of the air bubble at depth and
V₂ is the volume of the air bubble when it reaches the surface.
Rearrange the above equation to get the volume of the air bubble when it reaches the surface,
V₂= P₁V₁/Patm
Step: 1
Expression for the pressure at the depth is,
Substitute 1.0 atm for Patm and 2.0 atm for Pgauge
P₁ = 1.0 atm+ 2.0
=3.0
Explanation:
Pressure at the surface is calculated by adding gauge pressure and atmospheric pressure.
When the bubble rises from the depth of the lake, the temperature as well as pressure of the gas inside the bubble changes. This corresponds to the pressure of the water surrounding the bubble.
Hint:
Use the expression
V₂= P₁V₁/Patm
to calculate the volume of the air bubble when it reaches the surface.
Step: 2
The expression for the volume of the air bubble when it reaches the surface is,
Substitute
3.0 atm for
P₁= 1.6cm³ for
V₁ , and 1.0 atm
Patm= (3.0 atm ) (1.6cm³)/ (1.0 atm)
= 4.8cm³
Explanation:
The relation
P₁V₁= Patm V₂ is the also known as Boyle’s law.
Boyle’s law states that the pressure exerted by the given mass is inversely proportional to the volume it occupies if the amount of gas and temperature remains constant within a closed system.
Volume of the air bubble when it reaches the surface increases as compared to volume of the air bubble at depth.
The volume of the air bubble when it reaches the surface is
4.8 cm³
Therefore, the volume of the bubble as it reaches the surface is 4.8 cm³.
Learn more about volume from the given link.
https://brainly.com/question/28795033
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