The zilch cycle (due to Tony Arrott, of SFU) consists of two isotherms (in dark

Question

The zilch cycle (due to Tony Arrott, of SFU) consists of two isotherms (in dark blue), one adiabat (in red), and one isochor (in green), as shown at right. It has the curious feature that it produces no work; W cancels for the complete cycle because the areas enclosed on either side of the isochor are equal and navigated in opposite directions, thus cancelling each other out. P A B Assume 1 mol of an ideal monatomic gas. Starting at A the system expands isothermally at 600 K to point B. It is put in contact with a cold reservoir at 300 K so that it cools isochorically to point C. There is a further isothermal expansion to point D, followed by an adiabatic compression back to A. (a) Calculate WDA (b) Calculate QBC (c) Calculate WAB (d) Calculate WCD (e) what is the temperature at the intersection of the lines BC and AD?

Explanation / Answer

a)    WDA    =   0.02 * 1.013 * 105 * 300 * ln(5/2)

                  = 556921.5 J

b)   QBC   = 1 * 8.314 * 600 * ln(2/1)

                = 3457.69 J

c)   WAB   =   1 * 8.314 * 300 * ln(2/1)

                = 1728.84 J

d)   WCD   =    1 * 8.314 * 300 * ln(3/2)

                = 1011.31 J

e)   the temperature at the intersection of the lines BC and AD = 300 * (1728.84/1011.31)

                                                                                                  = 512.85 K

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