One mole of a monoatomic gas undergoes a linear process `A rarr B` in `P - v` diagram. The volume of the gas when the process turns from an endothermic to an exothermic one is

Options

A. `(5)/(8)v_(0)`
B. `(v_(0))/(2)`
C. `(8v_(0))/(15)`
D. `(3v_(0))/(5)`

Answer

A

Explanation

the point where adiabatic curve touch the line AB the nature of process will change from endo thermic to exothermic.

`-(P_(0))/(v_(0))=-gamma(P)/(V)`
`-m=-(gamma(-mv+P_(0)))/(V) m =+(P_(0))/(V_(0))`
`mv(1+gamma)=gammaP_(0) " " V=(gammaP_(0))/(m(1+gamma))=(5)/(8)V_(0)`