Two different adiabatic curves for the same gas intersect two isothermals at `T_(1), and T_(2)` as shown in `P-V` diagram, (figure). How does the ratio `(V_(a)//V_(d))` compare with the ratio `(V_(b)//V_(c))` ?

Answer

Same

Explanation

For adiabatic curve BC: `T_(1)V_(b)^((gamma-1))= T_(2)V_(c)^((gamma-1))`
For adiabatic curve AD: `T_(1)V_(a)^((gamma-1))= T_(2)V_(d)^((gamma-1))`
Dividing we get
`((V_(a))/(V_(b)))^((gamma-1))= ((V_(d))/(V_(c)))^((gamma-1)) or (V_(a))/(V_(b))=(V_(d))/(V_(c))`
`:. (V_(a))/(V_(d))=(V_(b))/(V_(c))`
i.e., the ratio remains the same.