To good approximation, the thermal conductivity k of a gas...

To good approximation, the thermal conductivity $k$ of a gas (see Ref. 21 of Chap. 1) depends only on the density $\rho$ mean free path $l$, gas constant $R$, and absolute temperature $T .$ For air at $20^{\circ} \mathrm{C}$ and 1 atm, $k \approx 0.026 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$ and $l \approx$ $6.5 \mathrm{E}-8 \mathrm{m} .$ Use this information to determine $k$ for hydrogen at $20^{\circ} \mathrm{C}$ and 1 atm if $l \approx 1.2 \mathrm{E}-7 \mathrm{m}$

To good approximation, the thermal conductivity $k$ of a gas (see Ref. 21 of Chap. 1) depends only on the density $\rho$ mean free path $l$, gas constant $R$, and absolute temperature
$T .$ For air at $20^{\circ} \mathrm{C}$ and 1 atm, $k \approx 0.026 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$ and $l \approx$ $6.5 \mathrm{E}-8 \mathrm{m} .$ Use this information to determine $k$ for hydrogen at $20^{\circ} \mathrm{C}$ and 1 atm if $l \approx 1.2 \mathrm{E}-7 \mathrm{m}$

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Key Concepts

Thermal Conductivity

Thermal conductivity quantifies a material's ability to transfer heat. In gases, it is influenced by the energy exchanged during molecular collisions and depends on factors like the density of the gas, the speed of the molecules (often a function of temperature), and how far molecules travel between collisions.

Mean Free Path

The mean free path is the average distance a gas molecule travels between successive collisions. It plays a key role in determining transport properties such as thermal conductivity because longer paths allow energy to be transported over longer distances, thereby enhancing the heat conduction capability.

Kinetic Theory of Gases

The kinetic theory of gases provides a framework for connecting microscopic molecular motions to macroscopic properties such as temperature, pressure, and thermal conductivity. It explains how molecular parameters, including velocity and mean free path, contribute to phenomena like heat transfer in gases.

Role of Density and Temperature

The density of a gas indicates the number of molecules available to conduct heat, while the temperature determines the kinetic energy of these molecules. Both properties, together with the gas constant, help define the energy per molecule and the overall efficiency of the thermal conduction process.

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