An air-standard Diesel cycle operates with a compression ratio, \(r=10: 1\). If the initial conditions at bdc are \(1 \mathrm{bar}\) and \(27^{\circ} \mathrm{C}\), and the energy addition is \(2000 \mathrm{~kJ} / \mathrm{kg}\) of air, calculate the salient points around the cycle, and the thermal efficiency. Show that the efficiency calculated from the cycle calculation is equal to that from Eqn (3.20). Assume the compression and expansion are isentropic and \(\kappa=1.4\). How does this compare with the efficiency of a Carnot cycle between the two temperature limits, and what is the value of \(\beta\) ? [45.02\%; 89.07\%; 3.6453]