A certain balloon maintains an internal gas pressure of `P_(0) = 100 k Pa` until the volume reaches `V_(0) = 20 m^(3)`. Beyond a volume of `20 m^(3)`, the internal pressure varies as `P = P_(0) + 2 k (V - V_(0))^(2)` where `P` is in `kPa`. `V` is n `m^(3)` and `k` is a constant `(k = 1 kPa//m^(3))`. Initially the balloon contains helium gas at `20^(@)C`, `100 kPa` with a `15 m^(3)` volume. The balloon is then heated until the volume becomes `25 m^(2)` and the pressure is 159 kPa. Assume ideal gas behaviour for helium. The work done by the balloon for the entire process in kJ is

Options

A. 1256
B. 1414
C. 1083
D. 1512

Answer

C

Explanation

c. Work done by the balloon
`W = int_(15 m^(3))^(20 m^(3)) P_(0) dV + int_(20 m^(3))^(25 m^(3)) PdV`
`= int_(15 m^(3))^(25 m^(3)) P_(0) dV + int_(20 m^(3))^(25 m^(3)) [P_(0) + 2 (V - V_(0))^(2)] dV`
`= [100 xx 5 + 100 xx 5 + 2 xx ((25 - 29)^(3))/(3)] kJ = 1083`