Question

During January, at a location in Alaska winds at -20°C can be observed, However, several meters below ground the temperature remains at 11°C. An inventor claims to have devised a power cycle working between these temperatures having a thermal efficiency of 10%.
Investigate this claim.

(a) What is the maximum thermal efficiency for these conditions?

(b) Is the inventor's claim possible?

Answer 1

Answer:

a) $\eta_{th} = 10.910\,\%$, b) Yes.

Explanation:

a) The maximum thermal efficiency is given by the Carnot's Cycle, whose formula is:

$\eta_{th} =\left(1-\frac{253.15\,K}{284.15\,K} \right) \times 100\,\%$

$\eta_{th} = 10.910\,\%$

b) The claim of the inventor is possible since real efficiency is lower than maximum thermal efficiency.