1 mole of an ideal gas `A(C_(v.m)=3R)` and 2 mole of an ideal gas B are `((C_(v,m)=(3)/(2)R)` taken in a container and expanded reversible and adiabatically from 1 litre of 4 letre starting from initial temperature of 320 K. `DeltaE ` or `DeltaU` for the process is :

Options

A. `240` R
B. 240 R
C. 480 R
D. `-960` R

Answer

D

Explanation

`"Av. C"_(V,m)=(n_(1)C_(V,m_(1))+n_(2)C_(V,m_(2)))/(n_(1)+n_(2))=2R`
for adiabatic process dU = dW
`(dT)/(T)=-(R)/(C_(V,m))((dV)/(V))`
`n_(1)C_(V,m_(1))dT+n_(2)C_(V,m_(2))dT`
`=-(n_(1)RT+n_(2)RT)xx(dV)/(V)`
`"ln"(T_(2))/(T_(1))=-(1)/(2)"ln"((V_(2))/(V_(1)))`
`rArr" "T_(2)=320xx((1)/(4))^(1//2)`
= 160 K
`DeltaU=(n_(1)C_(V,m_(1))+n_(2)C_(V,m_(2)))DeltaT=-960R`