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11. thermodynamics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics11. thermodynamics1 Mark
MCQ
In the reported figure, there is a cyclic process $ABCDA$ on a sample of $1\, {mol}$ of a diatomic gas. The temperature of the gas during the process ${A} \rightarrow {B}$ and ${C} \rightarrow {D}$ are ${T}_{1}$ and ${T}_{2}\left({T}_{1}\,>\,{T}_{2}\right)$ respectively.

Choose the correct option out of the following for work done if processes $B C$ and $D A$ are adiabatic.

  • A
    ${W}_{{AB}}\,<\,{W}_{{CD}}$
  • ✓
    ${W}_{{AD}}={W}_{{BC}}$
  • C
    ${W}_{{BC}}+{W}_{{DA}}\,>\,0$
  • D
    ${W}_{{AB}}={W}_{{DC}}$
✓

Answer

Correct option: B.
${W}_{{AD}}={W}_{{BC}}$
b
Work done in adiabatic process $=\frac{-n R}{\gamma-1}\left(T_{f}-T_{i}\right)$

$\therefore W _{ AD }=\frac{- nR }{\gamma-1}\left( T _{2}- T _{1}\right)$

$\text { and } W _{ BC }=\frac{- nR }{\gamma-1}\left( T _{2}- T _{1}\right)$

$\therefore W _{ AD }= W _{ BC }$

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