When `1mol` of a monoatomic ideal gas at `TK` undergoes adiabatic change under a constant external pressure of `1atm`, changes volume from `1 L to 2L`. The final temperature (in K) would be

Options

A. `T/((2)^(2//3))`
B. `T+2/(3xx0.0821)`
C. `T`
D. `T-3/(2xx0.0821)`

Answer

a

Explanation

`TV^(gamma-1)=K`
`:. T_(1)V_(1)^(gamma-1)=T_(2)V_(2)^(gamma-1)`
`T_(1)V_(1)^(2//3)=T_(2)V_(2)^(2//3)`
or `T_(1)(1)^(2//3)=T_(2)(2)^(2//3)`
or `T_(2)=(T_(1))/((2)^(2//3))=T/((2)^(2//3))`