Chapter 6, Problem 6.31P

Gases are often used instead of liquids to cool electronics in avionics applications because of weight considerations. The cooling systems are often closed so that coolants other than air may be used. Gases with high figures of merit (see Problem 6.30) are desired. For representative values of $m=0.85$ and $n=0.33$ in the expression of Problem 6.30, determine the figures of merit for air, pure helium, pure xenon $\left(k=0.006\text{W/m}\cdot \text{K,}\mu =24.14\times {10}^{-6}{\text{N×s/m}}^{\text{2}}\right),$ and an ideal He-Xe mixture containing 0.75 mole fraction of helium $\left(k=0.0713\text{W/m}\cdot \text{K,}\mu =25.95\times {10}^{-6}\text{N}\cdot {\text{s/m}}^{\text{2}}\right).$ Evaluate properties at 300 K and atmospheric pressure. For monatomic gases such as helium and xenon and their mixtures, the specific heat at constant pressure is well described by the relation $c_p=\left(5/2\right)\Re /M.$