Question

Engineers in Iceland are going green! They plan to build a heat engine which uses a natural hot spring as its heat source and wastes its heat to the chilly Icelandic atmosphere. The temperature of the hot spring is 31oC and ambient air temperature is 3oC. They estimate that the engine will exhaust 480kJ/s in waste heat. What is the maximum possible efficiency of this heat engine? What is the maximum power output that the engineers may expect?

Answer 1

The maximum possible efficiency of the heat engine is 9.21%, and the maximum power output that the engineers may expect is 480 kJ/s.

Step-by-step explanation:

To find the maximum possible efficiency of a heat engine, we can use the formula:

Emax = 1 - (Tcold / T)

where Tcold is the temperature of the cold reservoir and T is the temperature of the hot reservoir. In this case, the temperature of the hot spring is 31oC (or 304 K) and the ambient air temperature is 3oC (or 276 K). Plugging these values into the formula gives:

Emax = 1 - (276 / 304) = 0.0921 or 9.21%

To find the maximum power output, we can use the formula:

Pmax = Qin - Qout

where Qin is the heat energy input and Qout is the waste heat energy output. In this case, the waste heat is given as 480 kJ/s. Assuming this is the waste heat energy output, we can calculate the maximum power output as:

Pmax = 480 kJ/s