Two identical Carnot (cycles) engines operate between maximum and minimum temperatures $$T_1$$ and $$T_2$$ and volume limits $$V_a$$, $$V_b$$, $$V_c$$ and $$V_d$$ as shown in figure. Given that $$\frac{V_c}{V_a} = e^3$$ and $$\frac{T_1}{T_2} = e$$ (e is the base of natural logarithm). Engine 1 operates on mono atomic gas while the engine 2 on diatomic gas. Choose correct alternatives

A

Ratio of volumes $$\frac{V_{b,1}}{V_{b,2}} = e$$

B

Ratio of work done per cycle for the two is $$\frac{W_1}{W_2} = 3$$

C

Ratio of work per cycle for the two is $$\frac{W_1}{W_2} = 1$$

D

Ratio of efficiencies of two engines $$\frac{\eta_1}{\eta_2} = 1$$