Ocean Thermal Energy Conversion (OTEC) generates electricity using the difference between the temperatures at the surface of the ocean, where the water is warm, and far below the surface, where the water is cool. A test system off Hawaii operated between temperatures of 28.0 °C (the water temperature at the surface) and 4.00 °C.

Calculate the theoretical maximum efficiency (in percent) that you would expect for a system operating between those two temperatures.

Question

Ocean Thermal Energy Conversion (OTEC) generates electricity using the difference between the temperatures at the surface of the ocean, where the water is warm, and far below the surface, where the water is cool. A test system off Hawaii operated between temperatures of 28.0 °C (the water temperature at the surface) and 4.00 °C.

Calculate the theoretical maximum efficiency (in percent) that you would expect for a system operating between those two temperatures.

BlackTom AI · Accepted Answer

To assess the theoretical maximum efficiency for an energy-conversion process between two thermal reservoirs, we use the Carnot efficiency formula: η = 1 − Tc/Th, where temperatures are in Kelvin.

Step 1: Convert the given temperatures to Kelvin.
- Th (hot reservoir, surface water) = 28.0 °C + 273.15 = 301.15 K
- Tc (cold reservoir, deep water) = 4.00 °C + 273.15 = 277.15 K

Step 2: Compute the ratio Tc/Th.
- Tc/Th = 277.15 / 301.15 ≈ 0.9201

Step 3: Subtract from 1 to find the Carnot efficiency.
- η = 1 − 0.9201 ≈ 0.0799

Step 4: Convert to a percentage.
- η ≈ 7.99%

Notes:
- The calculation assumes an ideal Carnot engine with two reservoirs at the given temperatures; real systems typically have lower efficiencies due to irreversibilities and practical losses.
- Since there are no multiple-choice options provided here, we’ve shown the full calculation path and result one would compare to any options offered. The value aligns with the commonly cited maximum efficiency for this temperature pair around 8%.

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