Calculate the work done by the system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas `(gamma=4//3)` from 300 K and pressure 10 atm to 1 atm :

Options

A. `-227`
B. `-205 R`
C. `-405 R`
D. None of these

Answer

C

Explanation

`2xxC_(V,m)(T_(2)-T_(1))=-1((2RT_(2))/(1)-(2RT_(1))/(10))`
`gamma=(4)/(3)=(C_(p,m))/(C_(V,m))`
and `C_(p,m)=C_(V,m)+R" "therefore" "C_(V,m)=3R`
`"3 R"(T_(2)-300)=-RT_(2)+(Rxx300)/(10)`
`T_(2)=232.5K`
`w=DeltaU=2xx3R(300-232.5)`
`rArr" "w=-405R`