One way to improve insulation in windows is to fill a sealed space between two g
ID: 1648988 • 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 C_v, molar mass M, and molecular radius r. The dependence on those quantities at a given temperature is approximated by k proportionalto C_v/r^2 Squareroot M. 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.) he rate of effusion-that is, leakage of a gas through tiny cracks-is proportional to v_rms. If tiny cracks exist 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? 370 times 19 times 6 times No greater-the He leakage rate is the same as for X_e.Explanation / Answer
Since diffusion rate is directly proportion to Vrms and velocity is directly proportion to sqrt(M) , hence
Diffusion rate is directly proportion to sqrt(M)
d2/d1 = sqrt(M2/M1)
d2/d1 = sqrt(131/4)
d2 is 5.72 or approx 6 times greater than d1.
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