Question

For a Carnot engine with 10 moles of ideal gas (Cv= 1.5 nR) and operatingbetween a hot reservoir of 500 K and a cold reservoir of 300 K,a. (6 Points) What would be the heat exchanges (q1) and entropy change (∆S1) for step 1, where thegas reversibly and isothermally expands to double its volume (V2= 2 V1) at 500 K?b. (6 Points) What would be the heat exchanges (q3) and entropy change (∆S3) for step 3, where thegas is reversibly and isothermally compressed to half its volume (V4= 0.5 V3) at 300 K?c. (2 Points) What would be the net work done by this Carnot engine within each cycle?d. (2 Points) What would be the efficiency of this Carnot engine?

Answer 1

Ans:- (a Step 1 - a Step 1 ou reversible and is othermal expand on to volume double volume (W2= 2 ) at exchange, q = nk Thigh inf 2) q, = 10 x 8.314 x 500 lucevi) 2 = 28.814 KJP s 57.62 JK noopy charge , As, -a Trigle (6 is othconal compression for step 3 reversible and to half volane (V3 = 284) heat exchange, a = MR Teow luc V4) a 10x8.314x300 du =-17.288 kJ entropy change , As₂ = 2 =-57.62 J/K Tlow o for step 1 W - Q = - 28.814 Res. For step 2 w = new AT = 10x 1.5x8.314 8200) =-24.942 KJ. For step 3, Wes-Q = 17.288 kJ For step 4 W2 = norat = 10x1.5X8.3(4 x 200 = 24.992 kJ - w, tw,+ wat we = - 11.526 RS. Wretsystem

Whet cannot engine - MRT righ (lucra ) ) + ne T low ln (vey = . What system 11.526 kJ. (a) Efficiency = Whet heat engine - Wses heat absorbed by engine a , 11.526 KJ = 0.4 28. 814105 40% efficiency.