Question

An ideal monoatomic gas has taken round the cycle , work done during the cycle is:​

Answer 1

Assumptions :-

Let point A(P, V); B(4P, 3V); C(P, 3V)

Theory :-

Work done at constant volume = 0

Work done at constant pressure = P(V₂ - V₁)

For any general process,

Work done = Area under P- V curve

Calculation :-

From A to B, W$_{AB}$ = Area under P-V curve

                              = Area of trapezium

                              = $\frac{1}{2} (P + 4P)(3V-V)$

                              = 5PV

From B to C, W$_{BC$ = Done at constant volume

                              = 0

From C to A, W$_{CA$ = Done at constant volume

                              = P(V - 3V)

                              = -2PV

So, total work done during the cycle

= W$_{AB}$ + W$_{BC$ + W$_{CA$                                            

= 5PV + 0 + (-2PV)

= 3PV

Remarks :-

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