MCQ
One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-$I$ with the corresponding statements in List-$II$.
List-$I$ List-$II$
$P$ In process $I$ $1$ Work done by the gas is zero
$Q$ In process $II$ $2$ Temperature of the gas remains unchanged
$R$ In process $III$ $3$ No heat is exchanged between the gas and its surroundings
$S$ In process $IV$ $4$ Work done by the gas is $6 P _0 V _0$

  • A
    $P \rightarrow 4 ; Q \rightarrow 3 ; R \rightarrow 1 ; S \rightarrow 2$
  • B
    $P \rightarrow 1 ; Q \rightarrow 3 ; R \rightarrow 2 ; S \rightarrow 4$
  • $P \rightarrow 3 ; Q \rightarrow 4 ; R \rightarrow 1 ; S \rightarrow 2$
  • D
    $P \rightarrow 3 ; Q \rightarrow 4 ; R \rightarrow 2 ; S \rightarrow 1$

Answer

Correct option: C.
$P \rightarrow 3 ; Q \rightarrow 4 ; R \rightarrow 1 ; S \rightarrow 2$
c
$( P ) \rightarrow(3),( Q ) \rightarrow(4),( R ) \rightarrow(1),( S ) \rightarrow(2)$

$I \rightarrow$ adiabatic

$II$ $\rightarrow$ isobaric

$III$ $\rightarrow$ isochoric

$IV$ $\rightarrow$ isothermal

$(P)$ Process $I$ is adiabatic Hence No heat is exchanged between gas and surrounding.

$(Q)$ Process $II$ is isobaric.

$w = P \Delta V =3 P _0\left(3 V _0- V _0\right)=6 P _0 V _0$

$(R)$ Process is isochoric

$\Rightarrow w =0$

$(S)$ Process is isothermal $T =$ constant

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