At 30.0 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 0.80 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?
Use the combined gas law:
P1*V1/T1= P2*V2/T2 temps in Kelvins.
Pressure 30 m down can be figured this way.
Pressure= weight water above it+ atmospheric
= density*height + atmospheric pressure
oh yes, multiply the density by the gravational field constant to convert kg to N.
Pressure= density*g*height + atmospheric
A point source of light is 12 cm below the surface of a large body of water (n=4/3).
What is the radius of the largest circle on the water surface through which the light
can emerge?
25
To find the volume of the bubble just before it breaks the surface, we need to consider the effect of pressure and temperature changes.
Here's how you can find the volume of the bubble using the ideal gas law:
1. Convert the initial volume of the bubble to cubic meters:
Given volume = 0.80 cm^3 = 0.00000080 m^3
2. Calculate the initial pressure:
The pressure at 30.0 m below the surface is given by the hydrostatic pressure formula:
Pressure = density * gravity * height
where density = 1025 kg/m^3 and gravity = 9.8 m/s^2
Pressure = 1025 kg/m^3 * 9.8 m/s^2 * 30.0 m
3. Convert the initial pressure to Pascals (Pa):
Atmospheric pressure is typically defined as 101,325 Pa, so we need to add this value to the calculated pressure.
4. Convert the initial temperature to Kelvin (K):
The given temperature is 5.00°C, and we need to convert it to Kelvin by adding 273.15.
Initial temperature in Kelvin = 5.00°C + 273.15
5. Convert the surface temperature to Kelvin (K):
The given surface temperature is 20.0°C, so we convert it to Kelvin by adding 273.15.
Surface temperature in Kelvin = 20.0°C + 273.15
6. Use the ideal gas law equation:
PV = nRT, where:
P = pressure in Pa
V = volume in m^3
n = number of moles (which remains constant for this calculation)
R = universal gas constant, approximately 8.314 J/(mol K)
T = temperature in Kelvin
Rearranging the equation gives:
V = (nRT) / P
7. Calculate the volume of the bubble just before it breaks the surface:
Plug in the initial pressure, surface temperature, and the initial volume into the ideal gas law equation to find the final volume.
And that's how you can calculate the volume of the bubble just before it breaks the surface using the ideal gas law and the given conditions.