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.