Two different adiabatic parts for the same gas intersect two isothermals at `T_(1) "and" T_2` shown in P-V diagram . Then the ratio of `(V_(a))/(V_(b))` will be

Options

A. `(V_(c ))/(V_(d))`
B. `(V_(d))/(V_(c))`
C. `gamma(V_(d))/(V_(c))`
D. `(1)/(gamma)(V_(d))/(V_(c))`

Answer

B

Explanation

For adiabatic curve BC
`T_(1)V_(b)^(gamma-1)=T_(2)V_(C)^(gamma-1)`
Dividing (i) by (ii)
`(V_(b))/(V_(a))^(gamma-1)=(V_(C))/(V_(d))^(gamma-1) rArr (V_(a))/(V_(b))=(V_(d))/(V_(C))`