An ideal gas goes through a reversible cycle a → b → c → d which has… | JEE Main 2015 (10 Apr, Shift 1)

Q72JEE Main 2015 · 10 APR · SHIFT 1Difficult

P-V Diagrams & Cyclic Processes

An ideal gas goes through a reversible cycle a $\rightarrow$ b $\rightarrow$ c $\rightarrow$ d which has the V $-$ T diagram shown below. Process d $\rightarrow$ a and b $\rightarrow$ c are adiabatic.

The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale):

(A)

(B)

(C)

Numerical answer type. Work it out, then open the answer.

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Answer: a

$a \to b$ and $c \to d$ are straight lines through the origin on $V$ - $T$ , so $V \propto T$ : both are isobaric.
$a \to b$ : isobaric expansion at the higher pressure; $b \to c$ : adiabatic expansion ( $V$ up, $T$ down), so $P$ drops.
$c \to d$ : isobaric compression at the lower pressure; $d \to a$ : adiabatic compression back up to the higher pressure.
So $ab$ is the top horizontal line, $cd$ the bottom one, with adiabatic curves at the sides. The answer is (A).

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