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

Answer:

Not possible.

Explanation:

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

$\eta=1-\frac{T_{cold}}{T_{hot}}$

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) :

$\eta=1-\frac{-27+273}{14+273}\\=0.1428$

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.