An ideal gas undergoesa cyclic process from point A to point B to C to point D a

Question

An ideal gas undergoesa cyclic process from point A to point B to C to point D andback

to point A as shown inFigure below. The gas begins at a volume of 1.00 L and apressure

of 2.00 atm andexpands at constant pressure until the volume is 2.50 L, afterwhich it is

cooled at constantvolume until its pressure is 1.00 atm. It is then compressed atconstant

pressure until itsvolume is again 1.00 L, after which it is heated at constant volumeuntil

it is back in itsoriginal state. Find a) the total work done on the gas and b) thetotal heat

Explanation / Answer

(a) Since work done on the gas = W = -PV, W = Pa(Va-Vb) +Pc(Vc-Vd)       = 2(1-2.5) + 1(2.5-1) = -3 + 1.5 =-1.5 L-atm 1 L-atm = 10-3m3*1.01325105Pa = 101.325 J So, total work done on the gas = -152 J (b) Total change in internal energy is zero in a cyclicprocess. So, U = Q + W = 0 Q = heat supplied to the gas W = Work done on the gas Since W = -152 J, Q = -W = 152 J

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