# Problem 11-2 - Example 11-2 Derive the following expression...

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Example 11-2 Derive the following expression for the efficiency of the Diesel cycle in terms of the compression ratio, r v , and the cutoff ratio, r c () 1 1 1 1 1 k c cycle k vc r rk r η ⎡⎤ =− ⎢⎥ ⎣⎦ Solution: Start with this expression for the cycle efficiency: 4 1 1 3 2 2 1 1 1 cycle T T T T kT T ⎛⎞ ⎜⎟ ⎝⎠ eq (1) For the two adiabatic processes in the Diesel cycle 1 12 21 k TV = 1 3 4 34 k V T = But 14 VV = 23 P P = 2 22 mRT PV M = 3 33 mRT M = 2 2 3 3 P Vm R TT P R == VT =

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So 33 22 C TV r == eq. (2) 1 3 4 4 3 1 1 2 2 1 k k V T V T T V T V ⎛⎞ ⎜⎟ ⎝⎠ = but 14 VV = 1 1 3 42 13 4 k k C V TT r V 11 3 4 12 kk k CC T T rr −− = eq. (3) Finally 1 21 k = 1 2
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Problem 11-2 - Example 11-2 Derive the following expression...

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