One mole of an ideal monoatomic gas at `27^(@)C` is subjected to a reversible isoentropic compression until final temperature reaches `327^(@)C`. If the initial pressure was 1.0 atm then find the value of ln `P_(2)`:

Options

A. 1.75
B. 0.176
C. 1.0395
D. `2.0`

Answer

A

Explanation

Isoentropic `rArr q= 0 rArr T_(1)^(gamma), P_(1)^(1- gamma) = T_(2)^(gamma) P_(1)^(1- gamma)`
`(300)^(5//3) xx 1^((1-5//3)) = (600)^(5//3) xx P_(2)^((1- 5//3))`
`((1)/(2))^(5//3) = P_(2)^(-(2//3)) rArr (5)/(3)" ln" (1)/(2) = (-2)/(3) ln P_(2)`
`rArr ln P_(2) = (5)/(2) ln 2= 1.73`