`P-V` indicator diagram for a given sample of monoatomic idela gas is shown in figure. If the average molar specific heat capacity of the system for the process `ABCD` is `(xR)/(4)` than find value of `x:(R` is a uniersal gas constant)

Answer

9

Explanation

`Q_(AB) = - ((C_(p))p_(0)V_(0))/(R )`
`Q_(BC) = ((C_(v))p_(0)V_(0))/(R )`
`Q_(CD) = C_(p) (4p_(0)V_(0))/(R )`
Average molar specific heat capacity
`= (Q_(AB)+Q_(BC)+Q_(CD))/(mu(T_(D-T_(A)))) = [(3C_(p)+C_(v))/(4)]`