In the following P-V diagram two adiabatics cut two isothermals at temperature `T_(1) and T_(2)` (fig). The value of `V_(a)/V_(d)` will be

Options

A. `(V_(c))/(V_(b))`
B. `V_(C)V_(b)`
C. `(V_(b))/(V_(c))`
D. `(V_(c)V_(b))/(V_(c) + V_(b))`

Answer

C

Explanation

For curve be
`TV^(gamma-1) = "constant"`
`T_(1) V_(b)^(gamma-1) = T_(2) V_(v)^(gamma-1) "….."(1)`
For curved ad
`T_(1)V_(a)^(gamma-1)=T_(2)V_(d)^(gamma-1)"...."(2)`
eq. `(1)//(2) ((V_(b))/(V_(a)))^(gamma-1)=((V_(c))/(V_(d)))^(gamma-1)`
`rArr (V_(b))/(V_(a)) = (V_(c))/(V_(d))`
`rArr (V_(a))/(V_(d)) = (V_(b))/(V_(c))`