Mass of air breathed during diving

  • Thread starter TheBelgiumWaff
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In summary: Pv=nRTThe scuba diver has breathed in air with a mass of 288.7 kJ. After 20 minutes of breathing, the pressure in the air tank has decreased to 6 MPa and the temperature of the tank has dropped to 18 degrees Celsius.
  • #1
TheBelgiumWaff
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Homework Statement



Given: A scuba diver has a tank with an internal volume of 2500 cm^3 air tank which is pressurized to 22 MPa at 27 deg C. After diving for 20 minutes, she notices that the air pressure has reduced to 6 MPa while the temperature of the tank has dropped to 18 deg C.

Find: What is the mass of air that the diver has breathed through her lungs during the dive?


Homework Equations



P2*V2/T2 = P1*V1/T1 or Pv=nRT ?

The Attempt at a Solution



I'm confused which equation we use to find the solution and from there on how to punch in all the numbers to get to the solution.

I know the volume of air is 0.0883 m^3/Kmol, Rair = 0.2870 KJ/Kg*K, and mass = 28.97 kg/kmol
Also R = 8.314 KJ/Kg*K
I'm just really confused on where everything goes into play and why?
 
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  • #2
You should be able to use the first equation to get the volume of air left after 20 minutes. Once you get that volume then you can use PV=nRT or PV=mRairT
 
  • #3
rock.freak667 said:
You should be able to use the first equation to get the volume of air left after 20 minutes. Once you get that volume then you can use PV=nRT or PV=mRairT

When I found the volume it came out to be bigger than the original volume which doesn't feel right because I converted the cm^3 to m^3 and then switched to Kelvin for temp and the for the MPa conversion I did 10^3. Doing all this I came out with a volume that was 0.0088 m^3 roughly. Or is the volume supposed to be bigger?
 
  • #4
The first formula (general transformation of ideal gas) is obtained considering a process involving a fixed amount of gas.
This is not what you have here.
 
  • #5
nasu said:
The first formula (general transformation of ideal gas) is obtained considering a process involving a fixed amount of gas.
This is not what you have here.
Would I go about it the way rock described but only using the second part PV=mRairT?
 
  • #6
The volume of air in the tank is unchanged.
Find the mass before and after. And then the difference.
The mass is related to number of moles by n=m/M where M is the molar mass.
 
  • #7
I would separately calculate n from PV=nRT for the number of moles at the beginning and at the end. That would tell me how many moles of the air mixture were spent. Then multiply by the average molar mass of air (which you can calculate knowing air composition).

My bet is that the average molar mass of air is incorporated into Rair, but I never liked the idea of using separate R values for separate gases. It hides the generality of the ideal gas equation and Avogadro's hypothesis, leaving students confused.
 
  • #8
The universal R = 8.314 J/K*mol

MW air = 28.97 g/mol

Rair = (8.314 J/K*mol )/(0.02897 kg/mol) = 287 J/K*kg = 0.287 kJ/K*kg
 

What is "Mass breathed during diving"?

Mass breathed during diving refers to the amount of air or gas that a diver inhales and exhales while underwater. This includes both the volume of air and the weight of the gas.

How is mass breathed during diving measured?

Mass breathed during diving is typically measured in either liters or cubic feet of gas consumed. This measurement can be recorded using a submersible pressure gauge or through calculations based on tank pressure and volume.

What factors affect the mass breathed during diving?

The mass breathed during diving is affected by several factors, including the depth and duration of the dive, the diver's physical exertion, the type of gas used, and any equipment malfunctions or leaks.

Why is it important to monitor mass breathed during diving?

Monitoring mass breathed during diving is crucial for diver safety. It allows divers to track their air consumption and ensure they have enough gas to safely return to the surface. It also helps identify potential issues, such as equipment malfunctions, and allows for better planning of dives.

How can divers reduce their mass breathed during diving?

Divers can reduce their mass breathed during diving by improving their buoyancy control, using proper breathing techniques, and maintaining physical fitness. Choosing more efficient equipment, such as a low-resistance regulator, can also help reduce gas consumption.

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