A gas is taken through thecyclic process de- Find the net energy transferred to

Question

A gas is taken through thecyclic process de-

Find the net energy transferred to the system by heat during one complete cycle. Answer in units of kJ. If the cycle is reversed (that is, the process follows the path ACBA), what is the net energy transferred by heat per cycle? Answer in units of kJ.

Explanation / Answer

for a cycle, U = 0 U = q + W =>   q = -W Find the work, the area bounded by the curves. 1) Work from A -> B Find an expression for pressure as a function of V P - 4 kPa = [(12- 4) kPa/(11-6)m3 ]*[V - 6 m3] P - 4000 Pa = (8000 Pa/5m3)*(V - 6m3) P = 1600*V -5600Pa               Note V is in m3 Work = -integral [P*dV] = -integral[1600 V - 5600 Pa]*dV Work = [-800V2 + 5600 V]    evaluatedfrom VA = 6 m3, VB = 11m3 Work = [-800*112 + 5600*11] - [-800*62 +5600*6] Work = -40000 Joules 2) B -> C, Work = 0, because no change in volume 3) C -> A Work = -PV       P isconstant Work = -4000 Pa*(6 m3 - 11m3) = 20000 J ===== total work = -40000J + 20000J = -20000 Joules q = -total work = 20000 Joules = 2 x 104 Joules Note that you can easily find the work as just the are bounded bythe curve (area of the triangle: 0.5*base*height = 0.5*5m3*(8000 Pa) = 20000 Joules. It would be negative of thatthough) b) going in the opposite direction, q = -2 e4 Joules   (heatis removed from the system)

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