A heat engine runs in the cycle A to B to C and back to A as shown in the PV dia

Question

A heat engine runs in the cycle A to B to C and back to A as shown in the PV diagram.(Figure 1) The pressure at C is 200 kPa. The volume at C is 14 liters. The temperature at C is T K. The pressure at A is twice that at C. The volume at B is twice that at C. The internal energy at A and B are both 8400 J. The internal energy at C is 4200 J.

A) What is the work done in the transition A to B?

B) What is the work done in the transition B to C?

C) What is the TOTAL heat going into the gas during the cycle?

D) What is the total work done during the cycle?

E) What is the efficiency of this heat engine?

F) What is the efficiency of a Carnot cycle running between the lowest and highest temperatures of the cycle ABC?

Explanation / Answer

a) work done =area under graph = 200*v+0.5*v*200=300v=4200J b) frm B--C =200*V=2800J c) total work done during cycle=0.5*200v=-1400J total change in internal energy of cycle =0 so heat = 1400J D)total work done=-1400J e)100% f)highest temp at A and B ...lowest temp at C efficiency=1-1400/2800 = 50 %

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