Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $$\frac{V_a}{V_d}$$ and the ratio $$\frac{V_b}{V_c}$$ is:

A

$$\frac{V_a}{V_d} \neq \frac{V_b}{V_c}$$

B

$$\frac{V_a}{V_d} = \frac{V_b}{V_c}$$

C

$$\frac{V_a}{V_d} = \left(\frac{V_b}{V_c}\right)^{-1}$$

D

$$\frac{V_a}{V_d} = \left(\frac{V_b}{V_c}\right)^2$$