Modern vacuum pumps permit the pressures down to 4.1 × 10 -14 atm to be reached at room temperature (27°C). Assuming that the gas exhausted is nitrogen, find the mean distance between the gas molecule

Question

Modern vacuum pumps permit the pressures down to 4.1 × 10 -14 atm to be reached at room temperature (27°C). Assuming that the gas exhausted is nitrogen, find the mean distance between the gas molecules remained at this pressure.

TestHub · Accepted Answer

Number density N * = p/(kT) = ((4.1×10 -14 )/)(1.013×10 5 )(1.38×10 -23 )(300) ≈ 1.0×10 12 ,m -3 . Mean separation d ≈ (N * ) -1/3 = (1.0×10 12 ) -1/3 ,m = 10 -4 ,m = 0.01 cm. (The gas identity affects nothing here since only p and T enter.) Confirms Ans (c) 0.01 cm.

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