An ideal gas undergoes an expansion from a state with temperature `T_(1)` and volume `V_(1)` through three different polytropic processes `A, B` and `C` as shown in the `P - V` diagram. If `|Delta E_(A)|, |Delta E_(B)|` and `|Delta E_(C )|` be the magnitude of changes in internal energy along the three paths respectively, then :

Options

A. `|DeltaE_(A)| lt |DEltaE_(B) lt |DEltaE_(C)|` if temperature in every process decreases.
B. `|DeltaE_(A)| gt |DEltaE_(B) lt |DEltaE_(C)|` if temperature in every process decreases.
C. `|DeltaE_(A)| gt |DEltaE_(B) gt |DEltaE_(C)|` if temperature in every process increases
D. `|DeltaE_(B)| lt |DEltaE_(A) lt |DEltaE_(C)|` if temperature in every process increases

Answer

AC

Explanation

`DeltaE=nC_(v)DeltaT`
`DeltaT=(P_(2)V_(2)-P_(1)V_(1))/(nR)`
`rArr DeltaE=(C_(v))/R (P_(2)V_(2)-P_(1)V_(1))`
C has min. P.S. `E_(C) lt E_(B) lt E_(A)` if `DeltaT` is +ve.