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 approximated by k∝cv/(r2√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.) what is one reason the noble gases are preferable to air (which is mostly nitrogen and oxygen) as an insulating material? (a) noble gases are monatomic, so no rotational modes contribute to their molar heat capacity; (b) noble gases are monatomic, so they have lower molecular masses than do nitrogen and oxygen; (c) molecular radii in noble gases are much larger than those of gases that consist of diatomic molecules; (d) because noble gases are monatomic, they have many more degrees of freedom than do diatomic molecules, and their molar heat capacity is reduced by the number of degrees of freedom.