A small oxygen tank at a gauge pressure of 115 atm has a volume of 7.30 L at 17.

Question

A small oxygen tank at a gauge pressure of 115 atm has a volume of 7.30 L at 17.0 degree C. (a) If an athlete breathes oxygen from this tank at the rate of 8.30 L/min when measured at atmospheric pressure and the temperature remains at 17.0degree C, how long will the tank last before it is empty? hr (b) At a particular moment during this process, what is the ratio of the rms speed of the molecules remaining in the tank to the rms speed of those being released at atmospheric pressure? Vrms, tank/Vrms, released=

Explanation / Answer

a)

let the volume at atmospheric pressure is V2

Using ideal gas equation

P1 * v1 /T1 = P2 * V2/T2

115 * 7.30/(17 + 273) = 1 * V2 /(17 + 273)

V2 = 839.5 L

time to empty the tank = volume/volume flow rate

time to empty the tank = 839.5/8.30

time to empty the tank = 101.1 min

the time taken to empty the tank is 101.1 min

b) as the rms speed is gievn as

Vrms = sqrt(3 * RT/m)

as T is same for both tank and atmoshere

both Vrms will be same

Vrms,tank /Vrms,released = 1

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