Finding The Volume of An Air Bubble Just Before It Breaks Surface

[jasminstg]

At 24.0 m below the surface of the sea (density = 1025 kg/m3), where the temperature is 5.00°C, a diver exhales an air bubble having a volume of 0.90 cm3. If the surface temperature of the sea is 20.0°C, what is the volume of the bubble just before it breaks the surface?
_______ cm^3

 

[rl.bhat]

Use P1V1/T1 = P2V2/T2.

 

[kerimek]

Based on the given information, we can use the ideal gas law to calculate the volume of the air bubble just before it breaks the surface:

PV = nRT

Where:
P = pressure (in Pa)
V = volume (in m^3)
n = number of moles of gas
R = ideal gas constant (8.314 J/mol·K)
T = temperature (in K)

First, we need to convert the given values into the appropriate units:
- 24.0 m below the surface is equivalent to a pressure of 2.37 x 10^5 Pa (using the formula P = ρgh, where ρ is the density of seawater, g is the acceleration due to gravity, and h is the depth)
- 5.00°C is equivalent to 278.15 K
- 20.0°C is equivalent to 293.15 K

Next, we can calculate the number of moles of gas using the ideal gas law:
n = PV/RT = (2.37 x 10^5 Pa)(0.90 cm^3/100^3 m^3)/(8.314 J/mol·K)(278.15 K) = 3.61 x 10^-7 mol

Finally, we can plug in the new values into the ideal gas law to solve for the volume at the surface:
V = nRT/P = (3.61 x 10^-7 mol)(8.314 J/mol·K)(293.15 K)/(1.01 x 10^5 Pa) = 0.00000823 m^3 = 8.23 cm^3

Therefore, the volume of the air bubble just before it breaks the surface is approximately 8.23 cm^3. It is important to note that this calculation assumes that the temperature and pressure remain constant as the bubble rises to the surface. In reality, the bubble will likely expand due to the decreasing pressure, which may affect its volume just before it breaks the surface.