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(B) In the $P-T$ diagram, the lines passing through the origin represent isochoric processes (constant volume) because $P \propto T$ implies $V = 	ex

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$20$

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(B) In the $P-T$ diagram, the lines passing through the origin represent isochoric processes (constant volume) because $P \propto T$ implies $V = 	ext{constant}$.Thus, processes $1-2$ and $3-4$ are isochoric, and no work is done during these segments ($W_{1-2} = 0$, $W_{3-4} = 0$).Processes $2-3$ and $4-1$ are isobaric (constant pressure) because they are horizontal lines in the $P-T$ diagram.The work done in an isobaric process is $W = P\Delta V = nR\Delta T$.For the cycle, the total work done is $W_{	ext{total}} = W_{2-3} + W_{4-1}$.$W_{2-3} = nR(T_3 - T_2) = 3 	imes R 	imes (2400 - 800) = 3R(1600) = 4800R$.$W_{4-1} = nR(T_1 - T_4) = 3 	imes R 	imes (400 - 1200) = 3R(-800) = -2400R$.$W_{	ext{total}} = 4800R - 2400R = 2400R$.Using $R \approx 8.314\, J/(mol \cdot K)$:$W_{	ext{total}} = 2400 	imes 8.314 \approx 19953.6\, J \approx 20\, kJ$.

$3\, \text{moles}$ of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperatures in different states are: $T_1 = 400\, K$, $T_2 = 800\, K$, $T_3 = 2400\, K$ and $T_4 = 1200\, K$. The work done by the gas during the cycle is ...... $kJ$.

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