આપેલ \(\mathrm{P}-\mathrm{V}\) આલેખનો ઉપયોગ કરીને, પથ ABCD પર આદર્શ વાયુ દ્વારા થયેલું કાર્ય છે :

A \(3 \mathrm{P}_0 \mathrm{~V}_0\)
B \(-4 \mathrm{P}_0 \mathrm{~V}_0\)
C \(-3 \mathrm{P}_0 \mathrm{~V}_0\)
D \(4 \mathrm{P}_0 \mathrm{~V}_0\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(-3 \mathrm{P}_0 \mathrm{~V}_0\)

Step-by-step Solution

Detailed explanation

આલેખ હેઠળનું ક્ષેત્રફળ એ કાર્યનું માન દર્શાવે છે અને ઘડિયાળના કાંટાની વિરુદ્ધ દિશામાં હોવાને કારણે તે ઋણ હશે. \(\begin{aligned} & \text { Area }=2 P_0 \times V_0+P_0 V_0=3 P_0 V_0 \\ & \mathrm{~W}=-3 P_0 V_0 \end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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