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

Answer

D

Explanation

Aev. `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) = 320 xx ((1)/(4))^(1//2) = 160 K`
`Delta U = (n_(1)C_(v), m_(1) + n_(2)C_(V), m_(2))Delta T = -960 R`