The figure shows a reversible cycle through which 255 mol of

The figure shows a reversible cycle through which 2.55 mol of a monatomic ideal gas is taken. Assume that p = 2_p0,V = 2V_0,p0 = 4.50 x 10^5 Pa, and V_0 = 0.0211 m^3. Calculate (a) the work done during the cycle, (b) the energy added as heat during stroke abc, and (c) the efficiency of the cycle, (d) What is the efficiency of a Carnot engine operating between the highest and lowest temperatures that occur in the cycle? (e) Is this greater than or less than the efficiency calculated in (c)?

Solution

(a) the work done = area of the green square
                        W = P₀*V₀

                            = 9495 J
(b) heat energy is calculated as follows:

     Q = dU + Wbc = 3/2*R*(4T-T)+2P₀V₀ = 6.5P₀V₀ = 61717.5 J
(c)

efficiency is calculated as follows:

        e = W/Q = 9495 / 61717.5 = 15.38 %
(d)

ideal efficiency is calculated as follows:

e = efficiency of carnot engine = 1-T/4T= 0.75 = 75%

(e)

ideal efficiency in part d is greater than the efficiency in part c.