content_image/352200.jpg content_image/352201.jpg content_image/352202.jpg content_image/352203.jpg
With this substitution, our final result for the heating due to inelastic loss is 

<img src='content_image/352200.jpg'>

<img src='content_image/352201.jpg'>

If we assume that the ensemble stays in cross-dimensional equilibrium, T = T$_{z}$ = T$_{x}$ , then the overall heating rate is simply 

or equivalently, 

<img src='content_image/352202.jpg'>

<img src='content_image/352203.jpg'>

