In the following P–V diagram of an ideal gas, two adiabates cut two isotherms at `T_1` and `T_2` The value of `V_B // V_C` is :

Options

A. ` = V_A // V_D`
B. `lt V_A // V_D`
C. `gt V_A // V_D`
D. cannot say

Answer

A

Explanation

BC is adiabatic process
`T_1 V_B^(gamma -1) = T_2 V_C^(gamma -1)`
` T_1/T_2 = [V_C/V_B]^(gamma - 1)" ..(i)"`
Da is adiabatic process `T_2 V_D ^(gamma-1) = T_1 V_A^(gamma -1)`
`T_1/T_2 =((V_D)/(V_A))^(gamma -1)" ...(ii)"`
By Equation (i) and (ii)
`V_C = V_B = V_D /V_A " "V_B /V_C = V_A/ V_D`