One way to improve insulation in windows is to fill a sealed space between two g
ID: 1479737 • Letter: O
Question
One way to improve insulation in windows is to fill a sealed space between two glass panes with a gas that has a lower thermal conductivity than that of air. The thermal conductivity k of a gas depends on its molar heat capacity CV, molar mass M, and molecular radius r. The dependence on those quantities at a given temperature is approximately kCV/r2M. The noble gases have properties that make them particularly good choices as insulating gases. Noble gases range from helium (molar mass 4.0 g/mol, molecular radius 0.13 nm) to xenon (molar mass 131 g/mol, molecular radius 0.22 nm). (The noble gas radon is heavier than xenon, but radon is radioactive and so is not suitable for this purpose.)
The rate of effusion—that is, the leakage of a gas through tiny cracks—is proportional to vrms. If there are tiny cracks in the material that’s used to seal the space between two glass panes, how many times greater is the rate of He leakage out of the space between the panes than the rate of Xe leakage at the same temperature?
The rate of effusion—that is, the leakage of a gas through tiny cracks—is proportional to . If there are tiny cracks in the material that’s used to seal the space between two glass panes, how many times greater is the rate of leakage out of the space between the panes than the rate of leakage at the same temperature?
6 times 19 times 370 times No greater; the He leakage rate is the same as for Xe.Explanation / Answer
The Leakage rate is proportional to V rms as given
Leakage rate = VrmsHe/Vrms Xe =Sqrt(Mxe/MHe) = Sqrt(131.3/4) = 6
SIX (6) times greater is the rate of He leakage out of the space between the panes than the rate of Xe leakage at the same temperature
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