A cylindrical vessel of unifrom cross-section consisting of a gas of `gamma` =1.5 is divided into two parts A and B using a piston. Intially the piston is kept fixed such that part A has pressure p and volume 5 v and the part B has pressure 8 p and volume V. If the piston is let free and the gas is allowed to undergo adiabatic process, then the final volume of the gas in part A is

Options

A. `3V`
B. `8/3 V`
C. `10/3`V
D. `13/3` V

Answer

C

Explanation

Initially

For adiabatic expression in part A and B, we have ,
`p.(5V)^r = P_f V_A^( r)`
`8p. (V)^( R)= p_(f) . V_(B)^( r)`
Solving for `V_A` with `r= 1.5` We get `V_A = (10)/(3) V`