When one mole of a monoatomic ideal gas at initialtemperature T K expandsadiabatically from 1 litre to 2litres , the final temperature in Kelvin would be

When one mole of a monoatomic ideal gas at initialtemperature T K expa

1.	When one mole of a monoatomic ideal gas at initialtemperature T K expandsadiabatically from 1 litre to 2litres , the final temperature in Kelvin would be
Answer» <P>T `(T)/( 2^(2//3))` `T - (2)/( 3xx 0.0821)` `T + (2)/( 3 XX 0.0821)` Solution :`RV^(gamma-1)=` constant, i.e.,`T_(1)V_(1)^(gamma-1)= T_(2)V_(2)^(gamma-1)` or `(T_(2))/(T_(1))= ((V_(1))/(V_(2)))^(gamma-1)` or`(T_(2))/(T) = ((1)/(2))^((5)/(3)-1)= ( 1)/( 2^(2//3))` ( for monoatomic ideal gas , `gamma=(C_(p))/(C_(v))=((5//2)R)/((3//2)R)=(5)/(3))` `:. T_(2) =(T)/( 2^(2//3))`