Figure shows a cyclic process ABCDBEA. performed on an ideal cycle. lf $\mathrm{If} {\mathrm{P}}_{\mathrm{A}} = 2 \mathrm{atm}, {\mathrm{P}}_{\mathrm{B}} = 5 \mathrm{atm} \mathrm{and} {\mathrm{P}}_c = 6 \mathrm{atm}. {\mathrm{V}}_{\mathrm{E}}-{\mathrm{V}}_{\mathrm{A}}= 20 \mathrm{litre}$, find the work done by the gas in the complete, process (l atm. pressure = $1\times {10}^5$ Pa)

detailed solution

Correct option is A

The complete cyclic process can be visualized as made up of two cycles, i.e., cycle AEBA (clockwise) and cycle BDCB (counter-clockwise).Work done by the gas during the cycle AEBA should be positive,W1 = area of the loop in the P-V diagram      = 12(base)(altitude) = 12(VE-VA)(PB-PA)       = 12(20×10-3m3)(5-2)×105 Nm-2 = 3kJWork done by the gas the cycle BDCB should be negative,W2 = -(area of loop BDCB)Now evidently, triangles ABE and BCD are similar, the corresponding angles being equal (i.e.,