A diatomic gas expands adiabtically and final volume is 32 times of its volume . If initial termperature of the gas is `127 ^(@)` C , find the final termperature .

Explanation

For diatomic gas , ` gamma = (C_(p) ) /( C_(v ))=7/5`
initial temperature `T_(1 ) = 127 + 273 = 400 K`
In an adiabatic process ` TV ^( gamma -1)` constant
or `T_(2) V_(2) ^(gamma -1) = T_(1) V_(1) ^( gamma - 1) `
`or T_(2) = T_(1) ((V_1)/(v_2))^(gamma-1) = 400 xx((1)/(32))^(2//5)`
`=400 xx (1 )/( (2^(5) ) ^(2//5))=400 xx(1 )/(4) = 100 K `
`therefore ` final temperature `= ( 100 - 273 )^(@ ) C =- 17 3 ^(@)C `