The engine operates as follows: starting at point A with P = 2.0 x 10^5 Pa, V =

Question

The engine operates as follows: starting at point A with P = 2.0 x 10^5 Pa, V = 0.010 m^3, the gas is compressed to point B where the P = 4.0 x 10^5 Pa and V = 0.005 m^3. The gas is then isobarically expanded to 0.010 m^3 at point C. In the final step, the gas is isochorically expanded until the pressure is 2.0 x 10^5 Pa at point A. Show that segment AB is an isothermal compression. During which segment(s) is heat rejected by the gas? Calculate the temperature at points A, B, and C. Calculate the thermal efficiency of the engine.

Explanation / Answer

if the volumes are in liters and the pressures in kPa, we get

p V T pV

A 200 10 240.6 2000

B 400 5 240.6 2000

C 400 10 481 4000

Note: the product pV is the same for points A and B, so they are at the same temp

The product pV for point C is 4000, twice the value for point B, so the temp at C is double

Now, calc deltaE and work for each process, using deltaE = (5/2) (pV final - pVinitial)

deltaE W Q

AtoB 0 -1386 -1386

BtoC 5000 2000 7000

CtoA -5000 0 -5000

All of these values are in Joules. Work for each process was found using the appropriate expression for the process. For each line, Q is just deltaE + W (the first law of thermo).

Now to answer questions...

Temperatures are in the first table

Heat is rejected in both the AtoB and CtoA segments (i.e. Q is negative)

efficiency = total work / Q added to gas = (2000-1386) / 7000 = 8.77 %

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