Topic: Thermodynamics
During January, at a location in Rohtang, winds at $-6^{\circ}C$ can be observed. Several meters below the ground, the temperature remains at $27^{\circ}C$ A scientist claims to have devised a power cycle exploiting this situation that has a thermal efficiency of 10%. Whether the claim is true?
- A. True
- B. False
- C. Can't say
- D. Insufficient data
Answer: A. True
Explanation: The maximum possible thermal efficiency is given by the Carnot cycle efficiency $\eta = \frac{T_{max}-T_{min}}{T_{max}}$. Converting temperatures to Kelvin: $T_{max} = 27 + 273 = 300~K$ and $T_{min} = -6 + 273 = 267~K$. $\eta = \frac{300-267}{300} = \frac{33}{300} = 0.11 = 11\%$. Since the scientist's claimed efficiency (10%) is less than the theoretical maximum limit (11%), the claim is possible and thus true.