Estimate the value of the gas-phase diffusion coefficient for the following pairs using the Hirshfelder equation: a. Sulfur dioxide and nitrogen (N2) at 298 K and 1.5 x 105 Pa b. Hydrogen (H2) and air at 325 K and 2.0 x 105 Pa

a.

b.

Explanation:

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In this case, since the Hirschfelder's equation is:

Whereas M is the molar mass and sigma is related to the size of the molecule and omega the collision integral depending on the dimensionless temperature and are parameters related to the Chapman-Enskog theory and the Lenard-Jones parameters which have been tabulated for sulfur dioxide, nitrogen, hydrogen and air. Thus, we proceed as follows:

a. In this case, we have that sigma for sulfur dioxide is 4.026 and that of nitrogen is 3.667, and the parameter e/K is 363 K and 99.8 K respectively.

It means that the pairs are:

For which:

Based on Bird's E2 table.

Now, by plugging in the data, we obtain the following diffusion coefficient:

b. In this case, we have that sigma for hydrogen is 2.915 and that of air is 3.617, and the parameter e/K is 30.8 K and 97.0 K respectively.

It means that the pairs are:

For which:

Based on Bird's E2 table.

Now, by plugging in the data, we obtain the following diffusion coefficient:

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answer: semi-infinite solid initially at a uniform temperature of 400 ◦c is cooled at its surface by convection. the cooling fluid at a constant temperature of 200 ◦c has a convective coefficient (ha) of 250 w/m2.k. the physical properties of the solid: k = 20 w/m.k and α = 4 * 10-5  m2/s. using δx = 0.04 m and δt = 10 s. write the finite difference equations describing the transient heat transfer of the first five δx and the temperature profile after 30 s.