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_(b)/V_(c)`
B. `V_(c)/V_(b)`
C. `V_(d)/V_(a)`
D. `V_(b)V_(c)`

Answer

A

Explanation

For adiabatic process `T_(1) V_(b)^(gamma-1)` = constant
For `bc` curve `T_(1)V_(b)^(gamma-1) = T_(2)V_(C)^(gamma-1)` or `(T_2)/(T_1) = ((V_b)/(V_c))^(gamma-1)`
For `ad` curve `T_(1)V_(a)^(gamma-1) = T_(2) V_(c)^(gamma-1)` or `(T_2)/(T_1) = ((V_a)/(V_d))^(gamma-1)`
From equation (i) and (ii) , `(V_b)/(V_c) = (V_a)/(V_d)`.