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Worked Examples · Example 4.1

Q.The total work done in the cyclic process shown in Fig. 4.19 is −1000 J.

(a) What does the negative sign mean?
(b) What is the change in internal energy and the heat transferred during this process?
(c) What will happen when the direction of the cycle is changed?
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Figure — Maharashtra Board Std 12 Physics Thermodynamics: p-V diagram of a cyclic process between states A and B with two curved paths, total cyclic work done
FigureMaharashtra Board Std 12 Physics Thermodynamics: p-V diagram of a cyclic process between states A and B with two curved paths, total cyclic work done

A negative cyclic work means the loop is traversed counter-clockwise (work on the system); ΔU = 0 so Q = W = −1000 J; reversing direction flips the sign.

(a) The work done along A→B (expansion, volume increasing) is positive, and along B→A (compression) is negative and larger in magnitude, so the net work for the loop is negative — the loop is traversed counter-clockwise and net work is done ON the system.

(b) For any cyclic process the system returns to its starting state, so ΔU = 0. The first law then gives

Q=ΔU+W=0+(−1000)=−1000 JQ = \Delta U + W = 0 + (-1000) = -1000\ \mathrm{J}

so 1000 J of heat must be rejected by the system.

(c) If the direction of the cycle is reversed (made clockwise), the net work becomes positive: the system does work on the surroundings. A clockwise cyclic process does positive net work; a counter-clockwise one does negative net work.

✓Final answer

(a) Net work is done ON the system (counter-clockwise loop). (b) ΔU = 0, so Q = W = −1000 J (1000 J of heat is rejected). (c) Reversing the cycle makes the work positive.

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