Volume of Bubble: Solve for V2 at Depth of 30 m

In summary, a bubble with a volume of 1.00 cm3 forms at the bottom of a lake with a depth of 30 m and a temperature of 20°C. It rises to the surface where the water temperature is 35°C. Using the ideal gas law and assuming the bubble's temperature matches its surroundings, the volume of the bubble just before it breaks the surface is approximately 4.1448 cm3. This value was found by converting the temperatures to absolute temperature and using the equation P1V1/T1 = P2V2/T2.
  • #1
mikefitz
155
0

Homework Statement



A bubble with a volume of 1.00 cm3 forms at the bottom of a lake that is 30 m deep. The temperature at the bottom of the lake is 20°C. The bubble rises to the surface where the water temperature is 35°C. Assume that the bubble is small enough that its temperature always matches that of its surroundings. What is the volume of the bubble just before it breaks the surface of the water? Ignore surface tension.

Homework Equations



PV=nRT

P1V1/T1 = P2V2/T2

The Attempt at a Solution



P2 = 1atm
P1 = 1 atm + 1000 * 9.81 * 30 => 3.943atm

3.943atm*1cm3/20C = 1atm*V2/35C
V2=6.9cm3

This value for V2 is way too big, where did I screw up? Thanks
 
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  • #2
You've used celcius instead of absolute temperature.
 
  • #3
ahh

so,

3.943/293 = V2/308
V2=4.1448cm3?
 

Related to Volume of Bubble: Solve for V2 at Depth of 30 m

What is the formula for calculating the volume of a bubble at a depth of 30 m?

The formula for calculating the volume of a bubble at a depth of 30 m is V2 = (V1 * P2) / P1, where V1 is the volume of the bubble at the surface, P1 is the atmospheric pressure at the surface, and P2 is the pressure at a depth of 30 m.

How do I determine the volume of the bubble at a depth of 30 m if I only know the volume at the surface?

To determine the volume of the bubble at a depth of 30 m, you will need to use the formula V2 = (V1 * P2) / P1, where V1 is the known volume at the surface and P2 is the pressure at a depth of 30 m. You will also need to know the atmospheric pressure at the surface, P1.

What is the atmospheric pressure at the surface?

The atmospheric pressure at the surface can vary depending on location and weather conditions. The average atmospheric pressure at sea level is about 101.3 kilopascals (kPa) or 14.7 pounds per square inch (psi).

Can the volume of a bubble at a depth of 30 m be negative?

No, the volume of a bubble at any depth cannot be negative. The volume of a bubble is a physical quantity and cannot have a negative value. If you get a negative result when solving for V2, it may indicate an error in your calculations.

Why is it important to calculate the volume of a bubble at a depth of 30 m?

Calculating the volume of a bubble at a depth of 30 m can provide valuable information about the behavior of gases under pressure. It can also help in understanding the effects of depth on buoyancy and gas exchange in aquatic environments. Additionally, this calculation can be useful in various scientific and industrial applications, such as scuba diving and underwater construction.

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