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1 mole of an ideal gas A (C(v,m)=3R) and...

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 constainer and expanded reversible and adiabatically from 1 litre of 4 litre starting from initial temperature of 320K. `DeltaE or DeltaU` for the process is (in Cal) (Give your answer after divide with 240)

A

`240` R

B

240 R

C

480 R

D

`-960` R

Text Solution

Verified by Experts

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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