Question

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?

Answer 1

Answer: 624.98 mL

Explanation:

According to the Ideal Gas Law:

$\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}$ (1)

Where:

$P_{1}=2.4 atm$ is the pressure of the bubble under the surface

$V_{1}=250 mL$ is the volume of the bubble under the surface

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

$P_{2}=1 atm$ is the pressure of the bubble at the surface

$V_{2}$ is the volume of the bubble at the surface

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

So, we have to find $V_{2}$:

$V_{2}=\frac{P_{1}V_{1}T_{2}}{T_{1}P_{2}}$ (2)

$V_{2}=\frac{(2.4 atm)(250 mL)(300.15 K)}{(288.15 K)(1 atm)}$ (3)

Finally:

$V_{2}=624.98 mL$  This is the volume of the bubble when it reaches the surface

Answer 2

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:

$\large {\boxed {P = F \div A} }$

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:

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

$\frac{2.4(250)}{288} = \frac{1.0V_2}{300}$

$\frac{600}{288} = \frac{1.0V_2}{300}$

$\frac{25}{12} = \frac{V_2}{300}$

$V_2 = \frac{25}{12} \times 300$

$V_2 = 625 \texttt{ mL}$

$\texttt{ }$

Learn more

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