Question

During January, at a location in Rohtang, winds at -6°C can be observed. Several meters below the ground, the temperature remains at 27°C. A scientist claims to have device a power cycle exploiting this situation that has a thermal efficiency of 10%. Whether the claim is true?
1. True
2. False
3. Can’t say
4. Insufficient data

Answer 1

Correct Answer - Option 1 : True

Concept:

The following three conditions are followed to decide a device, whether it will function or not.

If η_claimed < η_carnot then the device will worked and possible  

If ηclaimed = ηcarnot then the device will have maximum 100% efficiency

If ηclaimed > ηcarnot then the device will not worked and impossible  

Calculation:

Given:

T_L = -6°C = 273-6 = 267 K, T_H = 27°C = 300 K, η_claim = 10 % 

\({η _{Carnot}} = \;1 - \frac{{{T_L}}}{{{T_H}}} = 1 - \frac{{267}}{{300}} = 0.11 = 11\% \)

\({η _{Claimed}} = 10\;\% \)

\(\;As\;{η _{claimed}} < {η _{Carnot}}\)

So the engine is possible.