An ideal gas is taken through a quasi-static process described by `P = alphaV^(2)`, with `alpha = 5.00 atm//m^(6)`. The gas is expanded to twice its original volume of `1.00 m^(3)`. How much work is done by the gas in expanding gas in this process?

Options

A. `1.8 MJ`
B. `2.18 MJ`
C. `1.28 MJ`
D. `3.18 MJ`

Answer

A

Explanation

The work done by the gas
`W = int_(i)^(f) PdV`
`W = int_(i)^(f) alpha V^2dV = 1/3 alpha(V_(f)^(3)-V_(i)^(3))`
`V_(f) =2V_(i) =2(1.00m^3) = 2.00m^(3)`
`W = 1/3[(5.00atm//m^(6))(1.013xx10^(5)Pa//at,=m)]`
`xx[(2.00m^3)^3-(1.00m)^(3))^(3)] = 1.18MJ`.