in the plane of the sky (as described above, Section \[pressure-results\]) the total lobe volume is $1.15\times10^{65}$ m$^3$. The energy stored in the lobes is then the energy density times the volume, or $9.1 \times 10^{52}$ J. Roughly equating the work done on the environment with 1/3 of this, we obtain $PV \approx 3.0\times10^{52}$ J or $3.0\times10^{59}$ ergs.

As we saw in Section \[outerregions\], the outer regions of the host group are cooler by $0.32 \pm 0.14$ keV than the regions at radii comparable to the extent of the lobes. We can use our estimate of the $PV$ work done by the lobes to ask whether this temperature difference is consistent with the idea that the radio source is heating the IGM in the inner part of the group.

Using the standard formulae for the proton number density in a $\beta$ model and the relation between the number of electrons and the number of protons (e.g. @bw93), we can calculate the thermal energy stored in a sphere of gas within the region that could plausibly have been affected by the radio source (region 1).

$$n_p=n_{p0}\left(1+\frac{r^2}{r_{cx}^2}\right)^{\frac{-3\ \beta}{2}}
\label{betamodel1}$$

$$n_e=1.18n_p$$

where $n_{p0}$ is the central proton number density which we obtain from 