Question

III. During January, at a location in Alaska winds at −27°C can be observed. However, several meters below ground the temperature remains at 14°C. An inventor claims to have devised a power cycle working between these temperatures having a thermal efficiency of 20%. Is it possible? Provide the corresponding calculation supporting your conclusion.

Answer 1

Not possible.

Step-by-step explanation:

According to second law of thermodynamics, the maximum efficiency any heat engine could achieve is Carnot Efficiency η defined by:

`\eta=1-(T_(cold))/(T_(hot))`

Where

`T_(hot)` and
`T_(cold)` are temperature (in Kelvin) of heat source and heatsink respectively

In our case (I will be using K = 273+°C) :

`\eta=1-(-27+273)/(14+273)\\=0.1428`

In percentage, this is 14.28% efficiency, which is the maximum theoretical efficiency any heat engine could have while working between -27 and 14 °C temperature. Any claim of more efficient heat engine between these 2 temperature are violates the second law of thermodynamics. Therefore, the claim must be false.