At which latitude heat gain through insolation approximately equals heat loss through terrestrial radiation :

Options

A. `22.5^(@)` North and South
B. `40^(@)` North and South
C. `42.5^(@)` North and South
D. `66^(@)` North and South

Answer

To solve the question of at which latitude heat gain through insolation approximately equals heat loss through terrestrial radiation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**:
- Heat gain through insolation refers to the energy received from the sun.
- Heat loss through terrestrial radiation refers to the energy lost back to space from the Earth's surface.

2. **Identify the Balance Point**:
- We need to find the latitude where the amount of heat gained equals the amount of heat lost, resulting in no net gain or loss of heat.

3. **Consider the Given Options**:
- The options provided are:
- 22.5 degrees North and South
- 40 degrees North and South
- 42.5 degrees North and South
- 66 degrees North and South

4. **Analyze Each Option**:
- At lower latitudes (like 22.5 degrees), there is generally more heat gain due to higher insolation.
- At higher latitudes (like 66 degrees), heat loss tends to exceed heat gain due to lower insolation and longer nights.
- The mid-latitudes (around 40 degrees) are where the balance is more likely to occur.

5. **Determine the Correct Latitude**:
- Based on the analysis, it is known that at approximately 40 degrees North and South, the heat gained through insolation is approximately equal to the heat lost through terrestrial radiation.

6. **Final Answer**:
- Therefore, the correct answer is **40 degrees North and South**.