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 :
A
`240` R
B
240 R
C
480 R
D
`-960` R
Text Solution
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The correct Answer is:
D
`"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`
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