A carnot engine maintains constant efficiency between 27 K and 527 K and between T K and 1054 K. Determine the unknown temperature.

Explanation

To solve for the unknown temperature \( T \) in the Carnot engine problem, we will follow these steps:

### Step 1: Write the formula for efficiency of a Carnot engine
The efficiency \( \eta \) of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{T_2}{T_1} \]
where \( T_1 \) is the temperature of the hot reservoir and \( T_2 \) is the temperature of the cold reservoir.
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