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A diver exhales a bubble with a volume of 250 mL at a pressure of 2.4 atm and a temperature of 15°C. What is the volume of the bubble when it reaches the surface where the pressure is 1.0 atm and the temperature is 27°C?

Respuesta :

cryssatemp

Answer: 624.98 mL

Explanation:

According to the Ideal Gas Law:

[tex]\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}[/tex] (1)

Where:

[tex]P_{1}=2.4 atm[/tex] is the pressure of the bubble under the surface

[tex]V_{1}=250 mL[/tex] is the volume of the bubble under the surface

[tex]T_{1}=15\°C + 273.15=288.15 K[/tex] is the temperature of the bubble under the surface

[tex]P_{2}=1 atm[/tex] is the pressure of the bubble at the surface

[tex]V_{2}[/tex] is the volume of the bubble at the surface

[tex]T_{2}=27\°C + 273.15=300.15 K[/tex] is the temperature of the bubble at the surface

So, we have to find [tex]V_{2}[/tex]:

[tex]V_{2}=\frac{P_{1}V_{1}T_{2}}{T_{1}P_{2}}[/tex] (2)

[tex]V_{2}=\frac{(2.4 atm)(250 mL)(300.15 K)}{(288.15 K)(1 atm)}[/tex] (3)

Finally:

[tex]V_{2}=624.98 mL[/tex]  This is the volume of the bubble when it reaches the surface

johanrusli

The volume of the bubble when it reaches the surface is about 625 mL

Further explanation

The basic formula of pressure that needs to be recalled is:

Pressure = Force / Cross-sectional Area

or symbolized:

[tex]\large {\boxed {P = F \div A} }[/tex]

P = Pressure (Pa)

F = Force (N)

A = Cross-sectional Area (m²)

Let us now tackle the problem !

In this problem , we will use Ideal Gas Law as follows:

Given:

Initial Volume = V₁ = 250 mL

Initial Pressure = P₁ = 2.4 atm

Initial Temperature = T₁ = 15 + 273 = 288 K

Final Pressure = P₂ = 1.0 atm

Final Temperature = T₂ = 27 + 273 = 300 K

Unknown:

Final Volume = V₂ = ?

Solution:

[tex]\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]

[tex]\frac{2.4(250)}{288} = \frac{1.0V_2}{300}[/tex]

[tex]\frac{600}{288} = \frac{1.0V_2}{300}[/tex]

[tex]\frac{25}{12} = \frac{V_2}{300}[/tex]

[tex]V_2 = \frac{25}{12} \times 300[/tex]

[tex]V_2 = 625 \texttt{ mL}[/tex]

[tex]\texttt{ }[/tex]

Learn more

  • Minimum Coefficient of Static Friction : https://brainly.com/question/5884009
  • The Pressure In A Sealed Plastic Container : https://brainly.com/question/10209135
  • Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454

Answer details

Grade: High School

Subject: Physics

Chapter: Pressure

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant , Liquid , Pressure

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