@George:2009; @Bautz:2009; @Hoshino:2010; @Kawaharada:2010]. Interpretations of these results include significant deviation from hydrostatic equilibrium and the effects of low thermalisation between electrons and ions in the cluster outskirts, especially where the edge of the cluster gas meets low-density regions [see @Kawaharada:2010 and references therein]. The entropy-based model presented here can easily be adapted to account for this observed behaviour at large radii by the introduction of additional parameters. For the purposes of this work we do not adapt the model for the results of the *Suzaku* observations, however in future work on CBI2 data we will consider the entropy behaviour at the cluster outskirts.

### The Pressure

If we assume that the gas particles of the intra-cluster medium are in local thermodynamic equilibrium, then the condition of hydrostatic equilibrium relates the total enclosed mass ($M$) to the electron density and partial pressure by $$\label{equation:HE}
{dP_\rmn{e}\over \rmn{d}r} = -{GM\mu m_\rmn{p}n_\rmn{e}(r)\over r^2},$$ where $\mu$ is the mean molecular mass per gas particle, which has a value of 0.6 for a fully ionised plasma with cosmic hydrogen and helium abundance ratios. From the expression given in Equation\[equation:entropy\_def\], and assuming the ideal gas law holds for the electron pressure (where $P_\rmn{e} =
n_\rmn{e}T_\rmn{e}$), the 