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The question is about the Carnot engine and its efficiency \( n \). For a Carnot engine, the efficiency \( n \) is defined as:

\[
n = 1 - \frac{T_2}{T_1}
\]

Where:
- \( T_1 \) is the temperature of the hot reservoir,
- \( T_2 \) is the temperature of the cold reservoir.

To solve for \( T_1 \), we can rearrange the efficiency formula:

\[
n = 1 - \frac{T_2}{T_1}
\]

Rearranging for \( T_1 \):

\[
\frac{T_2}{T_1} = 1 - n
\]

\[
T_1 = \frac{T_2}{1 - n}
\]

Thus, the correct expression for \( T_1 \) is \( \frac{T_2}{1 - n} \), which corresponds to option **3**.

Would you like more details or have any questions?

Here are five related questions:
1. What is the significance of the Carnot efficiency?
2. How is the efficiency of a Carnot engine related to real-world engines?
3. What are the assumptions made for a Carnot engine to achieve maximum efficiency?
4. How does the temperature difference between \( T_1 \) and \( T_2 \) affect the Carnot efficiency?
5. What happens to the efficiency as \( n \) approaches 1?

**Tip:** In any thermodynamic cycle, increasing the temperature of the hot reservoir or decreasing the temperature of the cold reservoir will increase efficiency.

A Carnot engine has an efficiency n and it operates between the temperatures T1 and T2. T1 and T2 are the temperatures of hot and cold reservoirs respectively. Which of the following is equal to T1?

Learn how to determine the temperature of the hot reservoir in a Carnot engine with a given efficiency. This problem covers thermodynamic concepts, including the Carnot efficiency theorem, and provides the formula to solve for T1. Suitable for students in Grades 11-12.

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