Question

A heat engine that propels a ship produces 400,000 lbf-ft/lbm while rejecting 300 btu/lbm of heat to a low temperature energy sink. Using what you know about heat engines, estimate its thermal efficiency?

Answer 1

The thermal efficiency of the ship's heat engine is estimated to be approximately 63.15% by calculating the ratio of work done to the total energy input (work done plus heat rejected), after converting the work done from lbf-ft/lbm to BTUs/lbm.

Step-by-step explanation:

To estimate the thermal efficiency of a heat engine propelling a ship, we use the basic definition of thermal efficiency for a heat engine, which is the ratio of work output to heat input. In this case, the engine produces 400,000 lbf-ft/lbm of work and rejects 300 BTU/lbm of heat. First, we need to convert the work done from lbf-ft/lbm to BTUs/lbm, using the conversion factor 1 BTU = 778.16 lbf-ft.

Work done (in BTUs/lbm) = 400,000 lbf-ft/lbm / 778.16 lbf-ft/BTU ≈ 514.19 BTUs/lbm

Now, the thermal efficiency (η) can be calculated using the formula:
η = Work done / (Work done + Heat rejected)

η = 514.19 BTUs/lbm / (514.19 BTUs/lbm + 300 BTUs/lbm)

η ≈ 0.6315 or 63.15%

Therefore, the estimated thermal efficiency of the heat engine is approximately 63.15%.