An ideal gas is taken through a quasi-static process described by $P = \alpha\, V^2$, with $\alpha = 5\,atm/m^6$. The gas is expanded to twice its original volume of $1\,m^3$. How much work is done by the expanding gas in this process
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$\mathrm{W}=\int_{\mathrm{V}_{1}}^{\mathrm{v}_{2}} \mathrm{P} \mathrm{d} \mathrm{v}$
$=5 \times 10^{5} \int_{1}^{2} \mathrm{V}^{2} \mathrm{d} \mathrm{v}$
$=5 \times 10^{5}\left[\frac{V^{3}}{3}\right]_{1}^{2}$
$=\frac{5}{3} \times\left[2^{3}-1^{3}\right] \times 10^{5} \mathrm{J}$
$=1018 \mathrm{MJ}$
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