A sample of ideal gas is expanded to twice its original volume of 1 m3 in a quasi-static process for which P = \(\alpha V^2\) with \(\alpha = \) 3 x 10⁵ Pa/m6 as shown in the given figure. Work done by the expanding gas is : 

7 x 10⁵ J

Work done : W = \(\int_{V_1}^{V_2} \alpha V^2 dV\)

... where \(\alpha = \) 3 x 10⁵ Pa/m⁶

W = \([\frac{\alpha V^3}{3}]^2_1\)

W = 10⁵ (V³₂ - V³₁)

V₁ = 1 m³ ; V₂ = 2 m³

W = 10⁵(8-1) = 7 x 10⁵ J