An ideal monoatomic gas indergoes a pressure `pV_(n)`=constant. The adiabatic constant for gas is `y`. During the process, volume of gas increases from `V_(0)` to `rV_(0)` and pressure decreases for `p_(0) ` to `(p_(0))/(2r)` Based on above information, answer the following questios :
The of n is

Options

A. `(2log r)/(log2r)`
B. `(log2 r)/(3)`
C. `(log2 r)/(log r)`
D. `(log2 r)/(3log r)`

Answer

C

Explanation

`Pv^(n)`=constant
Differentiating above equation, we get
` pxxnV^(n-1)dV+V^(n)dp=0 , np , dV=-Vdp`
`nint_(V_(0))^(rV_(0)) (dV)/(V)=-int_(p_(0))^(p_(0))(dp)/(p)impliesnlnr =-ln ((1)/(2r))`
`impliesn=("ln"2r)/("ln"r)`.