You Are Hired To Build A Geothermal Power Plant That

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The maximum (Carnot) efficiency of a heat engine is given by the formula: ( \text{efficiency} = 1 - \frac{T_C}{T_H} ), where (T_C) is the temperature of the cold reservoir and (T_H) is the temperature of the hot reservoir.

Given that the surrounding air temperature (T_C) is 14°C (287.15 K), and the maximum (Carnot) efficiency is 0.16, we can use the formula to calculate the temperature of the hot water spring ((T_H)).

Let's solve for (T_H):

[0.16 = 1 - \frac{287.15}{T_H}]

Solving for (T_H), we get:

[T_H = \frac{287.15}{1 - 0.16} = \frac{287.15}{0.84} ≈ 341.85]

So, the temperature of the hot water gushing from the spring should be approximately 341.85 K (68.70°C).

Therefore, the temperature in degrees Celsius of the hot water gushing from the spring is approximately 68.70°C.

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