A heat engine runs in the cycle A to B to C and back to A as shown in the PV dia
ID: 2118396 • Letter: A
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 is200 kPa. The volume at C is 13 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 7800 J. The internal energy at C is 3900 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
Volume of C = 13 lit = 13*10^-3 m^3
a)work done in the transition A to B = Area below AB line = 0.5(13*10^-3)(400+200)*10^-3 = 3900 J
b)work done in the transition B to C = Area below BC = -200*10^3 *13*10^-3=-2600 J
c)TOTAL heat going into the gas during the cycle = Heat going into gas during AB +BC+CA processes
Heat going into gas during AB = dU +dW = 3900 J
Heat going into gas during BC = dU +dW =(3900-7800) -2600 J = -6500 J, so heat is not going to gas here, it is being given by gas.
Heat going into gas during CA = dU +dW = (7800-3900)+0 = 3900 J
so, TOTAL heat going into the gas during the cycle = 3900 +3900 = 7800 J
d)work done during cycle = 3900-2600 = 1300 J
e)efficiency of heat engine = 1300/7800 = 1/6 = 0.1667
f) Highest temperature at A ,B .
Lowest temperature at C .
efficiency of carnot cycle = 1-(3900/7800) =0.5