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Heat Engine Practice Problem Problem Statement A piston-cylinder heat engine containing a monatomic ideal gas undergoes the three processes drawn on the p-V diagram below. The gas is initially at room temperature (300 K). What is the total work done by the gas and what is the total heat flow into the gas after completing one cycle? p (Pa) Visual Representation • Draw the pV diagram of the cycle (if not already given). 2 3000 2000 1000 درا V (m) 0 2. 3 Mathematical Representation • Determine p, V and T at the beginning and end of each process. • Calculate Q, Wby, and AEtherm for each process. Verify that (AEtherm)net=0. • Calculate desired quantities.

Answer 1

P(Pa) 3000 2000 To oo A 2 3 V6 Vi The work done by the gas W = Spor where p = pares sure infinitesimal change in volume. av - is the work done = Area under pr diagram. work done during the process AB TWAB Area under the carre AB = Arrear of triangle ABC & Area of rectangle (Achay) work done dursing the process CA TA = Area under ACVRY The negative sign shows the compressive work. Total work done w = WAB+ WeA = Arrea of the trange.

:. The net work done Arrea of the trotangh ABC (2* 2000) 2000T using The total heat flow can be calculated by the first haw of the modynamies AQ = 10+ AW AQ = AE + AW But for an or cyctic process DE=0 AQ= AW 200oJ Mathematical representation. ور & VITI) =( 1000 Pa, im, 300k) Pa/N9, T2 ) - (2000 Pa , 3mp, 1083 * temperature can be found out by wing the ideal gas equation. - PV T 3000 X 3 1083 K 8.31 . (@,V3, T) - (1060 Pa, 3 m3, 36) * T PV R 4000X3 8.31 = 361K

For the prouss 3 - 1 AQ = dut sw = 2R (T. - T3) {x8.31 (300-361) = - 760 J AQ = Autow AW= P(v. - V) 00(1-3) - 1000 =-2000J & Q = - 27605 A Enemas = AE, & AE₂ + OES = +9765+ - 9004 - 760 AW = AwtoW₂ 5W3 = 4000J +0 - 200 T AW= total 2oooT

AQ AQ, toQz+uQ, = 13,765 + - 9004 - 2760 2000 J