Heat Flux Between Two Parallel Plates

The heat capacity of N2 is about 20JK−1 mol−1 and its diffusion coefficient is 1.5 × 10−5 m2 s−1. How much heat will be conducted in 1 s across a 1-cm space between two parallel plates 2m2 in area if the plates differ in temperature by 5 K and the space between the plates is filled with nitrogen at 1 atm and 300 K? You may assume that the ideal gas law holds under these conditions.

“This is the problem 4.12 of the book “Chemical Kinetics and Reaction Dynamics, written by Paul L. Houston”.

According to the Fourier’s law, flux of heat across the space (labeled by z) between the plates, is proportional to the gradient of temperature across the space, i.e.,

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