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(D) For an adiabatic process, the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = 	ext{constant}$.Taking the natural logarith

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gas $B$ is monoatomic and gas $A$ is diatomic

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(D) For an adiabatic process, the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = 	ext{constant}$.Taking the natural logarithm on both sides, we get $\ln(PV^{\gamma}) = \ln(	ext{constant})$.This simplifies to $\ln P + \gamma \ln V = 	ext{constant}$, or $\ln P = -\gamma \ln V + 	ext{constant}$.Comparing this with the equation of a straight line $y = mx + c$, the slope $m$ is equal to $-\gamma$.From the given graph, the magnitude of the slope for $B$ is greater than the magnitude of the slope for $A$, i.e., $|	ext{slope}_B| > |	ext{slope}_A|$.Therefore, $\gamma_B > \gamma_A$.Since the adiabatic index $\gamma$ for a monoatomic gas is $1.67$ and for a diatomic gas is $1.4$, we conclude that gas $B$ is monoatomic and gas $A$ is diatomic.

The figure shows the graph of logarithmic reading of pressure and volume for two ideal gases $A$ and $B$ undergoing an adiabatic process. From the figure, it can be concluded that:

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