One mole of a diatomic.gas undergoes a process `p=(p_(0))/(1+((V)/(V_(0))^(3))`, where `p_(0)` and `V_(0)` are constants . The translational kinetic energy of the gas when V=`V_(0)` is given by

Options

A. `5 P_(0) V_(0)//4`
B. `3 P_(0) V_(0)//4`
C. `3 P_(0) V_(0)//2`
D. `5 P_(0) V_(0)//2`

Answer

B

Explanation

b. `P = (P_(0))/(1 + (V//V_(0))^(3))=(P_(0))/(2)`
`T = (P_(0) V_(0))/(2R)`
Therefore translational kinetic energy is equal to
`(3)/(2) RT = (3R)/(2) (P_(0) V_(0))/(2R) = (3P(0) V_(0))/(4)`