An adiabatic cyclinder fitted with an adiabatic piston at the right end of cylinder, is dicided into equal
halves with a monoatomic gas of the left side and diatomic gas on right side, using animpermeable movales
adiabatic wall , . If the piston is pushed slowely to compress the diatomic gas to `(3)/(4)th` of its origanl volume.
The new volume of the monoatomic gas would be.

Options

A. `V_("new")= V_("initial") xx[(4)/(3)]^((25)/(21))`
B. `V_("new")= V_("initial") xx[(7)/(5)]^((3)/(4))`
C. `V_("new")= V_("initial") xx[(3)/(4)]^((21)/(25))`
D. `V_("new")= V_("initial") xx(3)/(4)`

Answer

C

Explanation

`Pv^(gamma) = K`
for diatomic gas
`(P_(1))/(P_(2))=((V_(2))/(V_(1)))^(gamma)=((3)/(4))^(7//5)`
for monoatomic gas
`(P_(1))/(P_(2)) = (V_("new")/(V_("initial")))^(5//3) rArr V_("new") = V_("initial")xx ((3)/(4))^((21)/(25))`