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Two moles of an ideal monoatomic gas is taken through a cycle ABCA as shown in the P–T diagram. During process AB gas follows the process $P T^{2}$ = constant. Match the quantity in Column A with those in Column B.

Column-A
Column-B
A)
During process AB.
P)
$Δ U > 0$
B)
During process BC.
Q)
$W > 0$
C)
During process CA.
R)
$Δ Q < 0$
D)
During cyclic process ABCA.
S)
$Δ Q > 0$

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$A - R, B - P Q S, C - Q S, D - Q S$

$A - R Q, B - P Q S, C - Q S, D - Q R S$

$A - R, B - P S, C - Q S, D - Q R S$

answer is A.

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Detailed Solution

For AB, $P T^{2}$ = constant $\Rightarrow P V^{2 / 3}$ = constant
$C = \frac{R}{\frac{5}{3} - 1} + \frac{R}{1 - \frac{2}{3}} = \frac{3 R}{2} + \frac{3 R}{1} = \frac{9 R}{2}$
$Δ T = < 0$
$Δ Q < 0, Δ U < 0, W < 0$
For BC, $C = C_{P}$
$Δ U > 0, Δ Q > 0, W > 0$
For BC, $C = C_{P}$
$Δ U > 0, Δ Q > 0, W > 0$
For CA T = constant, $V_{A} > V_{C}$
$W > 0, Δ Q > 0, Δ U = 0$
For ABCA
$Δ U = 0, W > 0, Δ Q > 0$

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