The force $F$ between two electrically charge samples separated by a distance $r$ is:

$F=\frac{k_a{q}_1{q}_2}{r^2}$

where $k_a=8\mathrm{.}99{10}^{9}N.m^2.C^{-2}$ is the Coulomb force constant, $q_1$ and $q_2$ are charges.

An experiment $($Fig $1)$ is arranged whereby two identical electrical charges, each measuring $1$ mC $,$ are located $1$ metre apart. One charged

sample is secured firmly, whereas the other is attached to the piston part of a piston$-$cylinder $($air$-$filled$)$ and the resulting force of

electrostatic repulsion is in equilibrium with gas forces on the piston. The laboratory is housed in a satellite so that the laboratory pressure is

minimal. The cross$-$sectional area of the piston is $0\mathrm{.}04m^2$ and the piston cyliner initially contains $20$ litres of air at a temperature of $330$ K $.$

Fig. $1$ Piston$-$cylinder arrangement

The distance between the charges is to be reduced to $0\mathrm{.}8$ metres by means of heating the piston$-$cylinder.

Estimate the work done by the fluid on the charge during the expansion process. Give your answer in Joules to the nearest whole number.