One mole of an ideal gas undergoes a process `P = P_(0) [1 + ((2 V_(0))/(V))^(2)]^(-1)`, where `P_(0) V_(0)` are constants. Change in temperature of the gas when volume is changed from `V = V_(0) to V = 2 V_(0)` is:

Options

A. `4/5 (P_(0)V_(0))/(nR)`
B. `3/4 (P_(0)V_(0))/(n R)`
C. `2/3 (P_(0)V_(0))/(nR)`
D. `9/7 (P_(0)V_(0))/(nR)`

Answer

A

Explanation

`P =P_(0) [1+ (2V_(0) //V)"^(2)]^(-1)`
`At V=V_(0) , P =P _(0)//5 `
`T_(i) =(PV)/(nR) =((P_(0)//5)V_(o))/(nR) =(P_(o) V_(o))/(nR)`
` Delta T= T_(t) -T_(i) =(4P _(o)V_(o))/(5nR)`