Question 159 of 190

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



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

ABCD

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Answer: (A)

Is an adiabatic process

$T{V}^{\gamma -1}=const\Rightarrow V{T}^{\dfrac{1}{\gamma -1}}=const$

$\Rightarrow$ as T increase V decreases at non-uniform rate

In process $a\rightarrow b$ P = constant as $V\propto T$

In process $c\rightarrow d$ ${P}^{'}=$ constant s $V\propto T$

But since slope of V - T graph $\propto \dfrac{1}{P}$

since slope of ab < slope of cd

$\Rightarrow {P}_{ab}\gt {P}_{cd}$

Also in adiabatic process $d\rightarrow a$ as T is increasing V in decreasing

$\Rightarrow$ P is increasing, so P - V diagram is as below