 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2012/s4/2/b/solution

For the liquid pump take the explicit incompressible-water estimate

v_{f} ≃ 1 0^{- 3} m^{3} k g^{- 1}

. Its work input is

w_{p} ≃ v_{f} (P_{2} - P_{1}) = 1 0^{- 3} (28 - 0.002) 1 0^{6} = 27.998 kJ k g^{- 1},

h_{2} = h_{1} + w_{p} = 111.998 kJ k g^{- 1}

. With

h_{3} = 3463

and the preceding

h_{4} = 1838.74

in the same units,

q_{in} = h_{3} - h_{2} = 3351.002, w_{net} = h_{3} - h_{4} - w_{p} = 1596.26.

Thus

η = \frac{w _{net}}{q _{in}} = 0.47635 ≃ 47.6%.

If pump work is neglected because no liquid density was tabulated, the corresponding approximation is

(3463 - 1838.74) / (3463 - 84) = 48.1%

. Stating the approximation explains the small difference. The temperature-extreme Carnot efficiency is about

1 - 293.15/873.15 = 66.4%

, above both results; finite-temperature-range heat addition in the Rankine cycle does not attain that limit.

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