A sample of ideal gas is expanded to twice its original volume of `1.00 m^(3)` in a quasi-static process for which `P = alpha V^(2)`, with `alpha = 5.00 atm//m^(6)`, as shown in Fig. How much wor is done on the expanding gas ?

Options

A. `8 xx 10^(5) J`
B. `7 xx 10^(5) J`
C. `6 xx 10^(5) J`
D. `3 xx 10^(5) J`

Answer

B

Explanation

b. Work done, `W = int_(V_(1))^(V_(2)) alpha V^(2) dV`
where `alpha = 3 xx 10^(5) Pa//m^(6)`
`implies W = [(alpha V^(3))/(3)]_(V_(1))^(V_(2) = 2m^(3)) = [(3 xx 10^(5) V^(3))/(3)]_(V_(1))^(V_(2))`
`implies W = 10^(5) (V_(2)^(3) - V_(1)^(3))`
`V_(1) = 1 m^(3) V_(2) = 2 m^(3)`
`W = 10^(5) (8-1) = 7 xx 10^(5) J`