An ideal gas $$(0.5\ \mathrm{mol})$$, initially at $$2$$ bar pressure, is compressed at a constant temperature of $$600\ \mathrm{K}$$ in two steps: first, against a constant external pressure of $$P$$ bar $$(2 \lt P \lt 8)$$, and then against constant external pressure of $$8$$ bar. At each step, the compression is stopped only when the pressure of the gas becomes equal to the external pressure. The total work done on the gas in these steps is $$W$$. Considering all possible values of $$P$$ $$(2 \lt P \lt 8)$$ and taking the gas constant as $$R$$ (in $$\mathrm{J\ K^{-1}\ mol^{-1}}$$), the minimum value of $$|W|$$ (in $$\mathrm{J}$$) is
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