Question

Thirty-six grams of air in a piston–cylinder assembly undergo a Stirling cycle with a compression ratio of 7.5. At the beginning of the isothermal compression, the pressure and volume are 1 bar and 0.03 m3, respectively. The temperature during the isothermal expansion is 1200 K. Assuming the ideal gas model and ignoring kinetic and potential energy effects, determine the net work, in kJ.

Answer 1

The net work done during the Stirling cycle is 2.7 kJ.

Step-by-step explanation:

In order to determine the net work done during the Stirling cycle, we first need to calculate the initial and final volumes of the air in the piston-cylinder assembly.

Given:

1. Mass of air, m = 36 g = 0.036 kg
2. Initial pressure, P1 = 1 bar = 100,000 Pa
3. Initial volume, V1 = 0.03 m3
4. Compression ratio, r = 7.5
5. Temperature during isothermal expansion, TH = 1200 K

The compression ratio is given by:

r = V1/V2

where V2 is the final volume. Solving for V2, we get:

V2 = V1/r = 0.03/7.5 = 0.004 m3

Next, we can use the ideal gas law to relate the initial and final pressures and volumes:

P1V1/T1 = P2V2/T2

Since the process is isothermal, T1 = T2 = TH = 1200 K.

Solving for P2, we get:

P2 = (P1V1T2)/V2T1 = (100,000 x 0.03 x 1200)/(0.004 x 1200) = 100,000 Pa

Finally, we can calculate the net work done using the formula:

Wnet = (P1V1) - (P2V2)

Substituting the values, we get:

Wnet = (100,000 x 0.03) - (100,000 x 0.004) = 2700 J = 2.7 kJ