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?

Respuesta :

Answer:

a) [tex]\eta_{th} = 10.910\,\%[/tex], b) Yes.

Explanation:

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

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

[tex]\eta_{th} = 10.910\,\%[/tex]

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

The maximum thermal efficiency for the given conditions is; η_th = 10.91%

What is the maximum thermal efficiency?

A) The formula for maximum thermal efficiency is;

η_th = [1 - (T_c/T_h)] * 100%

We are given;

Cold temperature;T_c = -20°C = 253.15 K

Hotter temperature; T_h = 11°C = 284.15 K

Thus;

η_th = [1 - (253.15/284.15)] * 100%

η_th = 10.91%

B) We are told that the thermal efficiency is 10% but then we got a maximum thermal efficiency that is higher than the given efficiency. Thus, we conclude that;

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

Read more about Thermal Efficiency at; https://brainly.com/question/15901532